1 / 57

SWBAT… classify triangles in the coordinate plane

SWBAT… classify triangles in the coordinate plane. Agenda Warm-up: (10 min) Classifying triangles (40 min) Warm-Up: Write your HW in your planners Homework: Isosceles and Equilateral Triangles #1 – #8 #9: Is the triangle scalene, isosceles, or equilateral A(0, 1), B(4, 1), C(7, 0).

uriah
Télécharger la présentation

SWBAT… classify triangles in the coordinate plane

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. SWBAT… classify triangles in the coordinate plane Agenda Warm-up: (10 min) Classifying triangles (40 min) Warm-Up: Write your HW in your planners Homework: Isosceles and Equilateral Triangles #1 – #8 #9: Is the triangle scalene, isosceles, or equilateral A(0, 1), B(4, 1), C(7, 0) Thurs, 3/6

  2. Unit 5: Classifying Triangles

  3. Classification means put things into a group according to how they are alike.

  4. We will break this group of animals into smaller groups.

  5. Can't Fly Can Fly Extinct Still Living The same animals can be put into different groups depending on what we look at when we classify them.

  6. Today you will learn how triangles can be classified in two different ways...

  7. Think of all the different kinds of triangles you know. Acute Obtuse Right Scalene Isosceles Equilateral Did you come up with all of these?

  8. Triangle A polygon with 3 angles and 3 straight sides. The three endpoints are called vertices.

  9. Isosceles Scalene Equilateral at least two all 3 none Classifying by side lengths

  10. Scalene Triangle All sides are different lengths.

  11. Isosceles Triangle Two out of the three sides are equal lengths.

  12. Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

  13. Ex. If AC = BC, name two congruent angles.

  14. Equilateral Triangle All sides have the same length

  15. Properties of Equilateral Triangles A triangle is equilateral if and only if it is has three congruent angles (all the measures would then be 600.)

  16. Ex. KLM is an equilateral triangle with KL = d + 2, LM = 12 – d, KM = 4d – 13. Find d and the measure of each side. Example 1-3a 4d – 13 = d + 2 Substitution 3d – 13 = 2 Subtract d from each side. 3d = 15 Add 13 to each side. d = 5 Divide each side by 3. KL = 7, LM = 7, KM = 7

  17. Classify this triangle by its sides. ISOSCELES

  18. Classify this triangle by its sides. SCALENE

  19. EQUILATERAL Classify this triangle by its sides.

  20. Scalene Isosceles Equilateral Classify the following triangles by their sides. Use these signals:

  21. Scalene Isosceles Equilateral Classify by sides. Give the best name.

  22. Scalene Isosceles Equilateral Classify by sides. Give the best name.

  23. Scalene Isosceles Equilateral Classify by sides. Give the best name.

  24. What formula do you use to determine if a triangle is scalene, isosceles, or equilateral? Answer: The terms scalene, isosceles, and equilateral have to do with side lengths of a triangle so you use the Distance Formula.

  25. Obtuse Acute Right acute right obtuse Classifying by angle measures

  26. Acute Triangle 800 400 600 All three angles are less than 900.

  27. Obtuse Triangle 200 300 1300 One of the three angles is more than 900

  28. Right Triangle One of the three angles is exactly 900

  29. Acute Obtuse Right Classify the following triangles by their sides. Use these signals:

  30. Acute Obtuse Right Classify by angles.

  31. Acute Obtuse Right Classify by angles. 1000

  32. Acute Obtuse Right Classify by angles. 850 450 500

  33. E A B C D Now you should be able to classify any triangle by both its side lengths and its angles.

  34. Classify the triangles by sides lengths and angles 7 40° 15° 25 24 70° 70° 120° 45° • Solutions: • Scalene, Right • Isosceles, Acute • Scalene, Obtuse a) b) c)

  35. PQ = 2 2 ( – ) 6 (– 1 ) ) 3 – ( 2 7.1 + = = 2 2 2 – – – ( ( ( ) ) ) OP = + + + 2 2 2 – – – ( ( ( ) ) ) x y y x x y y x x x y y 1 2 2 1 1 2 1 1 2 2 2 1 2 2 ( – ( ) (– 1 ) ) 0 2 – 0 2.2 + = = 5 50 OQ = 2 2 ( – ( ) 6 ) 0 – 0 3 6.7 + = = 45 Example 1 Classify a triangle in a coordinate plane Determine whether PQOwith vertices at P(-1, 2), Q(6, 3), O(0, 0), is scalene, isosceles, or equilateral. Explain. Use the distance formula to find the side lengths. SOLUTION

  36. PQOis a scalene triangle since none of the sides are congruent. Explanation EXAMPLE Classify a triangle in a coordinate plane (continued)

  37. HW: Isosceles and Equilateral Triangles #1 – #8 #9: Is ABC scalene, isosceles, or equilateral A(0, 1), B(4, 1), C(7, 0)

  38. Using the ruler, draw triangles with the following side measures: a.) 3cm, 4cm, 6cm b.) 2cm, 2cm, 6cm

  39. Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Ex: Can these be the measures of a triangle? a.) 3cm, 4cm, 6cm b.) 2cm, 2cm, 6cm

  40. Example: Find value of x and missing side measurement

  41. Ex. Find the measure of each side of equilateral RST with RS = 2x + 2, ST = 3x, and TR = 5x – 4. 5x – 4 = 2x + 2 x = 2 RS = 6 ST = 6 TR = 6

  42. Ex. Find the measure of each side of isosceles ABC with AB = BC if AB = 4y, BC = 3y + 2, and AC = 3y. 3y + 2 = 4y y = 2 AB = 8 BC = 8 AC = 6

  43. Ex. Find x of isosceles right WZY if angle YWZ = 900, WZ = WY, and WYZ = 3x. 3x + 3x + 90 = 180 x = 15

  44. Example: Find missing angle measurements

  45. Example 1-2c Ex: Identify the indicated triangles in the figure. a. isosceles triangles Answer: ADE, ABE b. scalene triangles Answer: ABC, BCE, BDE, CDE, ACD, ABD c. equilateral triangles Answer: None!

  46. Exit Slip Is triangle A(0, 1), B(4, 4), and C(7,0) scalene, isosceles or equilateral. Explain. Answer: AB = 5 BC = 5 CA = 7.1 Since AB = Triangle ABC is isosceles since two of the sides are congruent.

  47. 6x0 2x0 #1 – #4: Find x: 600 3x + 8 400 4x – 4 (4x – 5)0 1.) 2.) 3.) 4.) 5.) Is triangle A(0, 1), B(4, 4), and C(7,0) scalene, isosceles or equilateral. Explain.

  48. SWBAT… classify triangles in the coordinate plane Agenda Warm-up: (10 min) 4 Examples (25 min) Review HW (10 min) Warm-Up: Find the missing angles: HW: Re-do 5 problems - Worksheet Mon, 3/10

  49. Warm-Up: What is Congruent? • AB  ________ • BD  _______  _______  _______ • CBE  ________ BCE • BDE  ________ • ABC ________

  50. Example: Find missing angle measurements

More Related