SlideServe
Télécharger Obtenir Pro
Menu
Accueil Pro
Préférences
ApparenceLight Aide et commentaires
© SlideServe · v2026

Triangles in Geometry: A Guide for 9th-10th Graders

lefty avatar
lefty
0 diapositives · 189 Views · Jul 08, 2014

Triangles with this engaging resource designed for 9th-10th graders. Created by Samantha Alberts, this guide targets middle-class suburban students preparing for geometry tests. It features interactive elements to cater to visual and kinesthetic learners, ensuring comprehensive understanding. Explore the properties, types, and applications of triangles in a simple and relatable manner. Perfect for study sessions, this material will enhance your grasp of triangle concepts and improve your performance in geometry.

#triangles #geometry #visual learning #kinesthetic learning #pythagorean theorem #test preparation #properties of triangles #math education
Triangles in Geometry: A Guide for 9th-10th Graders - slide 1
01 / 1Triangles in Geometry: A Guide for 9th-10th Graders
1 / 17

Télécharger la présentation

Triangles in Geometry: A Guide for 9th-10th Graders
Une image / un lien ci-dessous est fourni (tel quel) pour télécharger la présentation

Politique de téléchargement : le contenu du site vous est fourni TEL QUEL pour votre information et votre usage personnel ; il ne peut être vendu, concédé sous licence ni partagé sur d’autres sites sans l’accord de son auteur.Le contenu vous est fourni TEL QUEL, pour votre information et votre usage personnel uniquement. Téléchargez la présentation en cliquant sur ce lien. Lors du téléchargement, si vous ne parvenez pas à télécharger une présentation, l’éditeur a peut-être supprimé le fichier de son serveur.Pendant le téléchargement, si vous ne parvenez pas à obtenir une présentation, le fichier a peut-être été supprimé par l’éditeur.

F I N

Plus de contenu associé

Transcription de la présentation

  1. Triangles in GeometryClick anywhere to start!

    By: Samantha Alberts
  2. Audience 9th-10th graders Middle class suburban community Students who are studying for a test over triangles in geometry. Visual and kinesthetic learners Students who can regulate their own learning by adjusting their pace and amount of time on the lesson. Students who understand how to use a computer.
  3. Learning Environment Individually At a computer, during class In a computer lab calculator, pencil, and paper. In a place where learning and talking to oneself is allowed. Teacher walking around to aide when aide is needed.
  4. Objective (1) After reviewing the different types of triangles, students will be able to identify them with 100% accuracy.
  5. Objective (2) After reviewing the trigonometric functions students will be able to recognize how to use them with 95% accuracy.
  6. Objective (3) After reviewing the Pythagorean Theorem, the law of sines, and the law of cosines students will be able to demonstrate how to use each one with 85% accuracy.
  7. Objective (4) After going over special triangles students will be able to recognize them with 90% accuracy.
  8. Objective (5) Upon completion of this lesson students will be able to identify key types of triangles, special triangles, Pythagorean theorem, law of sines, and law of cosines with 80% accuracy.
  9. Objective (6) Upon completion of this lesson students will be prepared for their test on triangles by answering 80% of the quiz questions correctly.
  10. Motivation activity Do you think geometry is hard? Or that triangles are difficult? I have a solution. This lesson will allow all your questions to be answered. If not then you will receive a piece of candy for every question related to the material that will be on your test next week.
  11. Orientation activity In geometry triangles are very important. You will use them in almost all your math classes from here on. Make sure you pay attention to all the information. There will be a quiz at the end. Also, half the questions in the quiz will be on your test next week.
  12. Directions(please read all) Read through all the different information about each different section we covered in this part of the semester. Make sure you understand the material before going on to the next part, if that means you need to use your calculator, pencil, and paper then do so. You will later on in the lesson. Answer all the questions to the best of your ability. If you do well you are ready for the test. If not then go back over what you did not understand. Ask any questions when you have them.
  13. Help! This is the help page. Each button you see here will show up on other pages at the bottom. = back button Forward button= = Home button Home
  14. Home Page Pythagorean Theorem/ Non-right Triangles Interior & Exterior Angles Different Types of Triangles Special Triangles Right Triangles Quiz
  15. Interior & Exterior Angles An interior angle is inside the triangle. An exterior angle is created by extending any side of the triangle to the outside. Home
  16. Interior & Exterior Angles Home
  17. Interior & Exterior Angles The sum of all three interior angles in any triangle will always add up to 180˚. Home
  18. Interior & Exterior Angles ∠A=60˚ ∠D=120˚ Also, the sum of the interior angle and its exterior angle will always add up to be 180˚. 120˚ ∠A+∠D= 180˚ 60˚+120˚= 180˚ D A 60˚ Home
  19. Interior & Exterior Angles Question(Click on the answer you think it is) Is the interior angle the outside or inside angle of a triangle? A) Outside B) Inside
  20. Interior & Exterior Angles Question: Answer A) Outside INCORRECT. The interior angle is actually the inside angle of a triangle.
  21. Interior & Exterior Angles Question: Answer B) Inside CORRECT! The interior angle is the inside angle of a triangle.
  22. Interior & Exterior Angles Question(Click on the answer you think it is) Are the interior angle and exterior angle of a triangle equal to 180˚? A) Yes B) No
  23. Interior & Exterior Angles Question: Answer A) Yes CORRECT! The interior angle and the exterior angle added together equal 180˚
  24. Interior & Exterior Angles Question: Answer B) No INCORRECT! The interior angle and the exterior angle added together do equal 180˚
  25. Different Types of Triangles Equilateral Triangle: - Will always have 3 equal sides. Those sides will have equal angles. Those angles will always be 60˚. Home
  26. Different Types of Triangles Isosceles Triangle: - This triangle will always have 2 equal sides. Those 2 sides will always have the same angle. Home
  27. Different Types of Triangles Scalene Triangle: -Will never have any sides or angles the same. Home
  28. Different Types of Triangles Acute Triangle: -Will have every interior angle be less than 90˚ <90˚ Home
  29. Different Types of Triangles Obtuse Triangle: -Has one angle that is more than 90˚ Home
  30. Different Types of Triangles Question(Click on the answer you think it is) Is this an equilateral triangle? A) Yes B) No
  31. Different Types of Triangles Question: Answer A) Yes You are incorrect. Since the angles are different it is not an equilateral triangle. The triangle is actually an acute triangle.
  32. Different Types of Triangles Question: Answer B) No You are correct. An equilateral triangle has all the same angles. This triangle did not have all the same angles. It is actually an acute triangle.
  33. Different Types of Triangles Question(Click on the answer you think it is) Is this an acute triangle? A) yes B) No
  34. Different Types of Triangles Question: Answer A) Yes Oops! This triangle is actually an obtuse triangle. An acute triangle is actually less than 90˚
  35. Different Types of Triangles Question: Answer B) No Great job! You knew this was an obtuse triangle and not an acute triangle.
  36. Right Triangles Right Triangle: - Has one angle that is exactly 90˚ 90˚ Home
  37. Right Triangles Right Isosceles Triangle: - Has a right angle, as well as 2 equal angles that are 45˚ each. 45˚ 90˚ Home
  38. Right Triangles In right triangles, the trigonometric rations of sine, cosine, and tangent can be used to find unknown angles and the lengths of unknown sides. Home
  39. Right Triangles Home
  40. Right Triangles SinA= Opposite/ Hypotenuse Which equals =a/c Home
  41. Right Triangles CosA= Adjacent/ Hypotenuse Which equals =b/c Home
  42. Right Triangles TanA= Opposite/Adjacent Which equals =a/b Home
  43. Right Triangles “SOH-CAH-TOA” is easier to remember for sine, cosine, and tangent. SOH=> sin=opposite/hypotenuse CAH=> cos=adjacent/hypotenuse TOA => tan=opposite/adjacent Home
  44. Right Triangles CscA is the complete opposite of SinA so CscA=Hypotenuse/Opposite Which equals =c/a Home
  45. Right Triangles SecA is the complete opposite of CosA so SecA= Hypotenuse/adjacent Which equals =c/b Home
  46. Right Triangles CotA is the complete opposite of TanA so CotA=Adjacent/Opposite Which equals =b/a Home
  47. Right Triangles Question(Click on the answer you think it is) Is the SinH=A/C A) Yes B) No
  48. Right Triangles Question: Answer A) Yes CORRECT! The SinH is opposite/hypotenuse= A/C
  49. Right Triangles Question: Answer B) No INCORRECT. The SinH is equal to A/C, which is opposite/hypotenuse.
  50. Right Triangles Question(Click on the answer you think it is) Is the CotH=B/A A) Yes B) No
  51. Right Triangles Question: Answer A) Yes That’s Correct! The CotH is equal to B/A or Adjacent/Opposite
  52. Right Triangles Question: Answer B) No That’s Incorrect! The CotH is equal to B/A or Adjacent/Opposite
  53. Right Triangles Question(Click on the answer you think it is) Is this triangle a right or right isosceles triangle? A) Right Isosceles B) Right
  54. Right Triangles Question: Answer A) Right Isosceles Oops! It might look like a right isosceles triangle but the sides are not the equal and neither are the angles so it is actually a right triangle.
  55. Right Triangles Question: Answer B) Right Great job! You know that it was a right triangle because none of the sides or angles are the same.
  56. Pythagorean Theorem/ Non-right Triangles The Pythagorean Theorem is an equation that is used for right triangles only. It is used to find either a side or the hypotenuse. a and b are the sides or “legs” of the triangle and c is the hypotenuse. Home
  57. Pythagorean Theorem/ Non-right Triangles To use the Pythagorean Theorem you must identify the missing information. For example: You have the triangle with the information of b=4, a=3, and c=? What is c? ? 3 4 Home
  58. Pythagorean Theorem/ Non-right Triangles So you know that the Pythagorean Theorem is: c²=a²+b² You now plug in what you know from the given information. c²=3²+4² Home
  59. Pythagorean Theorem/ Non-right Triangles You then find the squares of 3 and 4 to get: c²=9+16 Then you add 9 and 16 together c²=25 Square root both sides √(c²)= √25 Your answer is: C=5 This is how you use the Pythagorean Theorem. Home
  60. Pythagorean Theorem/ Non-right Triangles Along with an equation for right triangles there are other equations for non-right triangles. These equations are called the law of sines and the law of cosines. The law of sines is useful for computing the lengths of the unknown sides in a triangle if two angles and one side are known. Home
  61. Pythagorean Theorem/ Non-right Triangles The equation for the law of sines is: sin A= sin B= sin C abc Home
  62. Pythagorean Theorem/ Non-right Triangles How to use the law of sines. If you have a non-right triangle with the known information of: A=60˚, B=80˚, C=40˚, a=6, b=?, c=? What do you do first? Let’s look and see. Home
  63. Pythagorean Theorem/ Non-right Triangles We are first going to find b then later we will find c. So we have the equation for law of sines. (You do not have to use the sin A = sin B whole equation) ab Then plug in what you know. sin 60 = sin 80 6 b Home
  64. Pythagorean Theorem/ Non-right Triangles You’re going to cross multiply to get: sin 60 = sin 80 Sin60b=Sin80(6) 6 b Which equals: Sin60b=5.9 Going to divide by Sin60 b=5.9/Sin 60 so the answer is: b=6.8 Home
  65. Pythagorean Theorem/ Non-right Triangles Then you need to solve for c by using either a or b to complete the triangle. Let’s use a because it was used in the problem to begin with and we know that it is correct. So you have: sin A= sin CSin60 =Sin40 ac 6 c Home
  66. Pythagorean Theorem/ Non-right Triangles You’re going to cross multiply to get: sin 60 = sin 40 Sin60c=Sin40(6) 6 c Which equals: Sin60c=3.9 Going to divide by Sin60 c=3.9/Sin 60 so the answer is: c=4.5 Home
  67. Pythagorean Theorem/ Non-right Triangles Along with the law of sines there is another equation known as the law of cosines, which can only be used for non-right triangles. The law of cosines can be used to determine a side of a triangle if two sides and the angle between them are known. It can also be used to find the cosine of an angle if the lengths of all the sides are known. There are three equations for the law of cosines. Home
  68. Pythagorean Theorem/ Non-right Triangles The law of cosines. c²=a²+b²-2abCosC This equation would be used to find the missing side c. Home
  69. Pythagorean Theorem/ Non-right Triangles How to use the law of cosines. For example you are given the following information. a=6, b= 2, CosC=56˚ You would use this equation to find c. Home
  70. Pythagorean Theorem/ Non-right Triangles You first plug in what you know from the information. c²=6²+2²-2(6)(2)Cos56 You simplify the equation c²=36+4-24Coc56 You simplify even more to get c²=40-14.11 Simplify one more time c²= 25.89 so the answer is C=5.09 Square root both sides √(c²)= √(25.89) Home
  71. Pythagorean Theorem/ Non-right Triangles There are two other equations for the law of cosines. Depending on what you are missing. If you are missing side a in the triangle the equation is a²= b²+c²-2bcCosA If you are missing side b in the triangle the equation is b²= a²+c²-2acCosB Home
  72. Pythagorean Theorem/ Non-right Triangles Question(Click on the answer you think it is) Do you use the Pythagorean Theorem for right triangles or non-right triangles? A) Right B) Non-right
  73. Pythagorean Theorem/ Non-right Triangles Question: Answer A) Right CORRECT! You do use the Pythagorean Theorem for right triangles.
  74. Pythagorean Theorem/ Non-right Triangles Question: Answer B) Non-right INCORRECT. The only time you do not use the Pythagorean Theorem is with non-right triangles.
  75. Pythagorean Theorem/ Non-right Triangles Question(Click on the answer you think it is) Is this the equation for law of sines? sin A= sin B= sin C bca A) Yes B) No
  76. Pythagorean Theorem/ Non-right Triangles Question: Answer A) Yes Oops! The law of sines equation is actually: sin A= sin B= sin C abc
  77. Pythagorean Theorem/ Non-right Triangles Question: Answer B) No Great job! You know that this is not the correct equation. The correct equation is: sin A= sin B= sin C abc
  78. Pythagorean Theorem/ Non-right Triangles Question(Click on the answer you think it is) If you were suppose to use the law of cosines to find b, would you use this equation? b²=a²-c²+acCosB A) Yes B) No
  79. Pythagorean Theorem/ Non-right Triangles Question: Answer A) Yes That’s incorrect. The real equation is b²=a²+c²-acCosB
  80. Pythagorean Theorem/ Non-right Triangles Question: Answer B) No That’s correct. The real equation is b²=a²+c²-acCosB
  81. Special Triangles There are a couple of special triangles that you will need to be aware of for your test next week. Home
  82. Special Triangles There is a special triangle with angles of 45-45-90. Which is called a 45-45-90 triangle. Which will always have a side ratio of 1:1:√2 Home
  83. Special Triangles Another special triangle that you need to know of is a 30-60-90 triangle. Which will always havea side ratio of 1:√3:2 Home
  84. Special Triangles There are also what we call “Pythagorean Triples” which are special triangles that will always be the same. Even their multiples are special triangles. Home
  85. Special Triangles Here are the three main Pythagorean Triples 3:4:5 5:12:13 8:15:17 But don’t forget that their multiples work too! 6:8:10 10:24:26 16:30:34 Home
  86. Special Triangles Question(Click on the answer you think it is) Does one of the special triangles have a side ratio of 1:1:√2? A) Yes B) No
  87. Special Triangles Question: Answer A) Yes CORRECT! The side ratio 1:1: √2 is that of a 45-45-90 triangle.
  88. Special Triangles Question: Answer B) No INCORRECT! The side ratio 1:1: √2 is that of a 45-45-90 triangle, which is a special triangle.
  89. Special Triangles Question(Click on the answer you think it is) Which one of these ratios is a Pythagorean Triple? A) 5:3:5.8 B) 3:4:5
  90. Special Triangles Question: Answer A) 5:3:5.8 Oops! The side ratio 5:3:5.8 is not a Pythagorean Triple.
  91. Special Triangles Question: Answer B) 3:4:5 Great job! The side ratio 3:4:5 is a Pythagorean Triple.
  92. Quiz Directions (Please read all) Before taking the quiz make sure you have a calculator, pencil, and paper. Once you start the quiz you can not go back till after the quiz is over. Also, keep track of which ones you get right and which ones you get wrong. You might see some of these questions on your test. Click here to being the quiz
  93. Question 1(click on your answer) What type of triangles are these? A) Equilateral B) Isosceles C) Scalene D) Right
  94. Question 1 Answer Oops! You chose A) Equilateral But an equilateral triangle has all the sides and angles equal to one another. These triangles has no equal sides or angles. Try again
  95. Question 1 Answer Oops! You chose B) Isosceles If you remember from the lesson an isosceles triangle has two equal sides and angles. These triangles have no equal sides or angles. Try again
  96. Question 1 Answer You’re Right! You chose C) Scalene A scalene triangle does not have any equal sides or angles! Question 2
  97. Question 1 Answer Oops! You chose D) Right Remember that a right triangle has one angle that is 90˚ like this. These triangles in the question have no sides or angles that are the same or an angle that is 90˚ Try again
  98. Question 2(click on your answer) What type of triangle is this? A) Acute B) Right C) Obtuse
  99. Question 2 Answer Great job! You chose A) Acute You know that an acute triangle had all its interior angles less than 90˚ Question 3
  100. Question 2 Answer Uh oh! You chose B) Right A right triangle has one angle that is 90˚. This triangle has all angles less than 90˚ Try Again
  101. Question 2 Answer Uh oh! You chose C) Obtuse An obtuse triangle has one angle that is more than 90˚. This triangle is less than 90˚. Try Again
  102. Question 3(Click on your answer) What type of triangles are these? A) Obtuse B) Acute C) Right
  103. Question 3 Answer You are incorrect. You chose A) Obtuse An obtuse triangle has one angle that is more than 90˚. These triangles have one angle that is exactly 90˚ each. Try Again
  104. Question 3 Answer You are incorrect. You chose B) Acute An acute triangle is less than 90˚. These triangles are exactly 90˚. Try Again
  105. Question 3 Answer You are correct. You chose C) Right A right triangle has one angle that is exactly 90˚. Question 4
  106. Question 4(click on your answer) What type of triangle is this? A) Isosceles B) Right C) Scalene D) Equilateral
  107. Question 4 Answer That’s not right. You chose A) Isosceles An isosceles triangle has only two sides and two angles that are the same. This triangle has all three sides and all three angles the same. Try Again
  108. Question 4 Answer That’s not right. You chose B) Right A right triangle has a 90˚angle. This triangle has no 90˚angle. In fact every side and angle are equal to one another. Try Again
  109. Question 4 Answer That’s not right. You chose C) Scalene A scalene triangle has no sides or angles that are the same. This triangle has all congruent sides and angles, means they are all the same. Try Again
  110. Question 4 Answer That’s right. You chose D) Equilateral An equilateral triangle has all congruent sides and angles, meaning they are all equal to each other. Question 5
  111. Question 5(click on your answer) What type of triangle is this? A) Obtuse B) Acute C) Right
  112. Question 5 Answer That’s Right! You chose A) Obtuse An obtuse triangle has an angle that is more than 90˚. Question 6
  113. Question 5 Answer That’s incorrect. You chose B) Acute An acute triangle has all its angles less than 90˚. This triangle has one angle that is more than 90˚. Try Again
  114. Question 5 Answer That’s incorrect. You chose C) Right A right triangle has an angle that is exactly 90˚. This triangle has an angle that is more than 90˚. Try Again
  115. Question 6(click on your answer) What type of triangle is this? A) Scalene B) Isosceles C) Right D) Equilateral
  116. Question 6 Answer That is incorrect. You chose A) Scalene A scalene triangle has no sides or angles that are the same. This triangle has two sides and two angles that are the same. Try Again
  117. Question 6 Answer That is Correct. You chose B) Isosceles An isosceles triangle has two sides and two angles that are the same. Question 7
  118. Question 6 Answer That is incorrect. You chose C) Right A right triangle has one angle that is exactly 90˚. This triangle has no angle that is 90˚. Try Again
  119. Question 6 Answer That is incorrect. You chose D) Equilateral An equilateral triangle has all three sides and all three angles the same. This triangle has only two sides and two angles that are the same. Try Again
  120. Question 7(click on your answer) What does SOH-CAH-TOA stand for? A) Some - Canned - Tofu B) Sin= opp/hyp - Cos=adj/hyp - Tan=opp/adj C) Symmetric - Congruent - Tangent
  121. Question 7 Answer That’s not right. You chose A) Some-Canned-Tofu Someone’s not been paying attention. I think you are thinking about lunch. Try Again
  122. Question 7 Answer That’s right. You chose B) Sin= opp/hyp-Cos=adj/hyp-Tan=opp/adj SOH-CAH-TOA stands for how to find the different sides of a right triangle. Question 8
  123. Question 7 Answer That’s not right. You chose C) Symmetric-Congruent-Tangent I can see where it might mean this. However, that isn’t what SOH-CAH-TOA stands for. Try Again
  124. Question 8(click on your answer) What is the sinA? B A) 4/5 5 B) 3/5 4 C) 3/4 D) 5/4 C A 3
  125. Question 8 Answer You’re correct! You chose A) 4/5 4/5 is the sinA Question 9
  126. Question 8 Answer You’re incorrect You chose B) 3/5 3/5 is actually the CosA not the SinA Try Again
  127. Question 8 Answer You’re incorrect You chose C) 3/4 3/4 is the TanA not the SinA Try Again
  128. Question 8 Answer You’re incorrect You chose D) 5/4 5/4 is the CscA not the SinA Try Again
  129. Question 9(click on your answer) What is the TanC? C 1 B A) 1/√3 B) 2/√3 √3 2 C) √3/1 D) √3/2 A
  130. Question 9 Answer That’s not quite right You chose A) 1/√3 1/√3 is the CotC not the TanC Try Again
  131. Question 9 Answer That’s not quite right You chose B) 2/√3 2/√3 is the CscC not the TanC Try Again
  132. Question 9 Answer That’s right You chose C) √3/1 √3/1 is the TanC Question 10
  133. Question 9 Answer That’s not quite right You chose D) √3/2 √3/2 is the SinC not the TanC Try Again
  134. Question 10(click on your answer) What is the SecB? C 6 A A) 6/10.8 B) 10.8/6 10.8 9 C) 9/10.8 B D) 10.8/9
  135. Question 10 Answer Oops! You chose A) 6/10.8 6/10.8 is the SinB not the SecB Try Again
  136. Question 10 Answer Oops! You chose B) 10.8/6 10.8/6 is the CscB not the SecB Try Again
  137. Question 10 Answer Oops! You chose C) 9/10.8 9/10.8 is the CosB not the SecB Try Again
  138. Question 10 Answer Yay! You chose D) 10.8/9 10.8/9 is the SecB Question 11
  139. Question 11(click on your answer) What is the CscA? A) 5/4 B B)5/3 5 4 C) 4/5 A 3 C D) 4/3
  140. Question 11 Answer Correct! You chose A) 5/4 5/4 is the CscA Question 12
  141. Question 11 Answer That is incorrect. You chose B) 5/3 5/3 is the SecA not the CscA. Try Again
  142. Question 11 Answer That is incorrect. You chose C) 4/5 4/5 is the SinA not the CscA. Try Again
  143. Question 11 Answer That is incorrect. You chose D) 4/3 4/3 is the TanA not the CscA. Try Again
  144. Question 12(click on your answer) Use the Pythagorean Theorem to find the missing side. B A) 16 17 B) 8 15 C) 9 C A ?
  145. Question 12 Answer That’s not quite right You chose A) 16 16 is not the missing side. Try to use the Pythagorean Theorem again. Try Again
  146. Question 12 Answer That’s right You chose B) 8 8 is the missing side of this triangle. This triangle is also a Pythagorean Triple if you remember. Question 13
  147. Question 12 Answer That’s not quite right You chose C) 9 9 is not the missing side. Try to use the Pythagorean Theorem again. Try Again
  148. Question 13(click on your answer) Find the missing information using the Law of Sines. A=60˚ a=6 B=80˚ b=6.8 C= 40˚ c=? A) 4.5 B) 5 A b c C) 4.7 B C a
  149. Question 13 Answer Great job! You chose A) 4.5 4.5 is the missing side. Question 14
  150. Question 13 Answer Uh oh! You chose B) 5 5 is not the missing side. Try to use the law of sines again start with; Sin60 = Sin40 6 c Try Again
  151. Question 13 Answer Uh oh! You chose C) 4.7 4.7 is not the missing side. Try to use the law of sines again start with; Sin60 = Sin40 6 c Try Again
  152. Question 14(click on your answer) Use the law of cosines to find the missing information. What is a equal to? A) 255.6 6 55˚ B) 257 15 a C) 259.7
  153. Question 14 Answer Oops! You chose A) 255.6 255.6 is not the missing side. Try to use the law of cosines again start with; a²=6²+15²-2(6)(15)Cos55 Try Again
  154. Question 14 Answer Great job! You chose B) 257 257 is the missing side. Question 15
  155. Question 14 Answer Oops! You chose C) 259.7 259.7 is not the missing side. Try to use the law of cosines again start with; a²=6²+15²-2(6)(15)Cos55 Try Again
  156. Question 15(click on your answer) Which angle is the exterior angle? A) ∠A B B) ∠B C) ∠C D A C D) ∠D
  157. Question 15 Answer Uh Oh! You chose A) ∠A ∠A is an interior angle not an exterior angle. Try Again
  158. Question 15 Answer Uh Oh! You chose B) ∠B ∠B is an interior angle not an exterior angle. Try Again
  159. Question 15 Answer Uh Oh! You chose C) ∠C ∠C is an interior angle not an exterior angle. Try Again
  160. Question 15 Answer Awesome job! You chose D) ∠D ∠D is an exterior angle. Question 16
  161. Question 16(click on your answer) What do all the interior angles add up to? A) 90 B) 180 C) 270 D) 360
  162. Question 16 Answer That’s not quite right. You chose A) 90 90 is to small for all the interior angles to add up to because you can have one interior angle that is 90 or larger. Try Again
  163. Question 16 Answer That’s right. You chose B) 180 180 is what all the interior angles add up to be. Question 17
  164. Question 16 Answer That’s not quite right. You chose C) 270 270 is to large for all the interior angles to add up to. Try Again
  165. Question 16 Answer That’s not quite right. You chose D) 360 360 is to big for all the interior angles to add up to. Try Again
  166. Question 17(click on your answer) If you have an interior angle of 39˚ what is your exterior angle? A) 51˚ B) 141˚ C) 231˚ D) 321˚
  167. Question 17 Answer You‘re incorrect You chose A) 51˚ 51˚ only makes 90˚ which is to small. Try Again
  168. Question 17 Answer You‘re correct You chose B) 141˚ 141˚ is what the exterior angle is. Question 18
  169. Question 17 Answer You‘re incorrect You chose C) 231˚ 231˚ is to much for the exterior angle to be. Try Again
  170. Question 17 Answer You‘re incorrect You chose D) 321˚ 321˚ is to much for the exterior angle to be. Try Again
  171. Question 18(click on your answer) What is the ratio for a 45-45-90 triangle? A) 1:√3:2 B) 7:15:18 C) 1:1:√2 D) 3:4:5
  172. Question 18 Answer Oops! You chose A) 1:√3:2 1:√3:2 is a special triangle ratio, but not for a 45-45-90 triangle. Try Again
  173. Question 18 Answer Oops! You chose B) 7:15:18 7:15:18 is not a possible triangle. Try Again
  174. Question 18 Answer Great job! You chose C) 1:1:√2 1:1:√2 is the ratio for a 45-45-90 triangle. Question 19
  175. Question 18 Answer Oops! You chose D) 3:4:5 3:4:5 triangle is a special triangle but its angles are not 45-45-90 Try Again
  176. Question 19(click on your answer) What is the ratio of a 30-60-90 triangle? A) 1:√3:2 B) 1:1:√2 C) 8:15:17 D) 3:4:5
  177. Question 19 Answer You‘re right. You chose A) 1:√3:2 1:√3:2 is the ratio of a 30-60-90 triangle. Question 20
  178. Question 19 Answer You‘re not right. You chose B) 1:1:√2 1:1:√2 is the ratio of a 45-45-90 triangle. Try Again
  179. Question 19 Answer You‘re not right. You chose C) 8:15:17 8:15:17 is a special triangle but its not the ratio of a 30-60-90 triangle. Try Again
  180. Question 19 Answer You‘re not right. You chose D) 3:4:5 3:4:5 is a special triangle but its not the ratio of a 30-60-90 triangle. Try Again
  181. Question 20(click on your answer) Is a 32:60:68 triangle a Pythagorean Triple? A) Yes B) No
  182. Question 20 Answer Yay! You chose A) Yes 32:60:68 is the same triangle as 8:15:17 just multiplied by 4
  183. Question 20 Answer Uh oh! You chose B) No 32:60:68 is the same triangle as 8:15:17, which is a Pythagorean Triple, it’s just multiplied by 4
  184. Since You finished! Here is a video to show another way to remember the Pythagorean Theorem.
  185. Congrats You’ve Finished the Quiz!Let’s see how you did! If you got 20 right you’re amazing! If you got 17-19 right you’re very smart! If you got 14-16 right you did a good job. If you got 10-13 right you need to go over something in the lesson again. If you got 0-9 right go back through the information and try again.
  186. You got 14-20 Questions Right! You know your triangles! Please come see me to find out what you need to do next. Home
  187. You got 0-13 Questions Right Need to go back over something you didn’t know or understand? Click the home button to go back to the home page. Also, ask questions if you don’t understand where you went wrong. Home