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Homework: Collected. 10. x. 3. 6. 4. x. What do you know about the Pythagorean Theorem? Formula? When and why it’s used? Solve for x :. SWBAT… classify triangles in the coordinate plane. Agenda Notes – 2 slides (20 min) 4 examples (15 min) Exit slip (15 min) Warm-Up:

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## Homework: Collected.

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**Homework: Collected.**10 x 3 6 4 x • What do you know about the Pythagorean Theorem? • Formula? • When and why it’s used? • Solve for x:**SWBAT… classify triangles in the coordinate plane**Agenda Notes – 2 slides (20 min) 4 examples (15 min) Exit slip (15 min) Warm-Up: Write your HW in your planners Set up your Cornell Notes. Topic is “Pythagorean Theorem” Homework: Pg. 495: #7 – 18, 24 – 32 Thurs, 3/13**Who was he?**Greek mathematician named Pythagoras Born ~569 BC on the Greek island of Samos Founded a school for the study of philosophy, mathematics and science. Used mathematics as a means to understand the natural world - First to teach that the earth was a sphere that revolves around the sun Today, the Pythagorean Theorem is one of the most famous theorems in geometry. The relationship it describes has been known for thousands of years.**c**a b Pythagorean Theorem • In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. • a2 + b2 = c2 • Side “a” and “b” are called the legs (can be switched around) • Side “c” is called the hypotenuse. • Side “c” must always be the longest side • Side “c” is always opposite the right angle (900)**When do I use the Pythagorean Theorem?**If I know the length of any two sides of a right triangle and I need to know the length of third side**The Pythagorean Theorem**• “For any right triangle, the sum of the areas of the two small squares is equal to the area of the larger.” • a2 + b2 = c2**a2 + b2 = c2**152 + 202 = x2 225 + 400 = x2 625 = x2 Ex: Find the length of the hypotenuse x 15 20**a2+ b2 = c2**62+ x2= 102 36 + x2= 100 -36 -36 x2= 64 x = 8 Ex: Find the length of the leg 10 6 x**a2 + b2 = c2**102 + 242 = x2 100 + 576 = x2 676 = x2 26 = x Ex: The legs of a right triangle have lengths 10 and 24. What is the length of the hypotenuse? x 10 24**Ex: Is the triangle a right triangle?Explain.**28 20 19 a2 + b2 = c2 202 + 192 = 282 400 + 361 = 784 761 = 784 Answer: NO, because a2 + b2 does not equal c2**Pythagorean Triples**Whole numbers a, b, and c that satisfy the equationa2 + b2 = c2. Some common Pythagorean Triples: 3, 4, 5 5, 12, 13 8, 15, 17 7, 24, 25**Ex: Do 16, 48, and 50 form a Pythagorean Triple?**a2+ b2 = c2 162+ 482= 502 256 + 2304 = 2500 2560 = 2500 Answer: No, since 16, 48, and 50 did not satisfy a2 + b2 = c2**Determining Type of Triangle:**If c2 = a2 + b2 then you know it is a right triangle. If c2 > a2 + b2 then you know it is an obtuse triangle. If c2 < a2 + b2 then you know it is an acute triangle.**Ex. Is the triangle with side lengths 4,**acute, right or obtuse? c2 a2 + b2 42 + 16 7 + 11 16 < 18 Answer: Since c2 < a2 + b2, the triangle is acute.**Exit slip: Collected**Page 495: #1 – #6 HW: Pg. 495: #7 – 18, 24 – 32**Error Analysis:**A triangle has side lengths of 16, 34, and 30. Your friend says it is not a right triangle. Look at your friends work and describe the error. 162+ 342= 302 256 + 1,156 = 900 1,412 = 900**Warm-Up: What is Congruent?**• AB ________ • BD _______ _______ _______ • CBE ________ BCE • BDE ________ • ABC ________**Tim rode 8 miles due north, then 3 miles due east. How far,**to the nearest mile, is Tim from where he started? Draw a picture: a2 + b2 = c2 82 + 32 = c2 64 + 9 = c2 73 = c2 3 8 x c = 8.5440037 Tim is 9 miles from where he started.**a2 + b2 = c2**x2 + 52 = 152 x2 + 25 = 225 - 25 -25 x2 = 200 x = 14.142135 The ladder reaches 14.1 feet up the wall. Draw a picture: 15 x A 15 foot ladder leans up against a building. The foot of the ladder is 5 feet from the base of the building. How high up the wall does the ladder reach? 5**Draw a picture and solve:**a2 + b2 = c2 32 + 42 = c2 9 + 16 = c2 25 = c2 3 4 x 4 3 5 = c The length of each side of the rhombus is 5 cm. The diagonals of a rhombus are 6 cm and 8 cm. What is the length of each side of the rhombus?**A person can travel from NYC to Buffalo by going north 170**miles to Albany and then west 280 miles to Buffalo. If a highway is built to connect NYC and Buffalo, how many miles would be saved on the trip?**Find length of new highway**Old Distance: 280 + 170 = 450 New Distance: 327.566 Saved Miles: 122.4 or 122 miles 280 miles Albany 170 miles ??? New York City a2 + b2 = c2 2802+1702=c2 107300 m= c2 Buf 327.566= c Did I answer question? How many miles would be saved?**B) With gas prices at $3.10 and a vehicle that gets 18 mpg,**how much money would be saved roundtrip, if the new highway was traveled instead of the old route? • Saved Miles: 122 miles x 2 = 244 • Cost to drive one mile (gas): • $3.10 divided by 18. ($0.1722…) • Cost to drive 244 miles • $0.1722 times 244 • Saved: $42.02**Warm-Up: What is Congruent?**• 1. If AB BC, name two congruent angles. _______ and _______ • 2. If ACD ADC, name two congruent segments. ______ and ______**Warm-UpFind the missing angles:**450 900 x = ______ y = ______**The slope ofOPis**2 – 0 3 – 0 1 . – 2. The slope ofOQis = = – 2 – 0 2 6 – 0 Using slopes, determine if PQO is a right triangle. Explain. SOLUTION • Check for right angles by checking the slopes. • There is a right angle in the triangle if any of the slopes are perpendicular. Explanation PQOis a right triangle because the slopes of the legs have opposite signs and reciprocals which means they are perpendicular and form a right angle.**Name the missing coordinates of isosceles right triangle**ABC. C(0, 0) A(0, d)**Applying the Pythagorean Theorem Answers**x = 15 km x = 10 blocks x = 8.5 in x = 8.7 m x = 32.2 ft x = 90.1 ft x = 8.5 ft x = 96 ft x = 101.8 ft x = 24.9 in**Applying the Pythagorean Theorem**11. x = 30 in. No, the box is too small. 12. x = 340 ft 13. x = 8.2 ft 14. x = 8.1 mi 15. Yes, it is a right triangle because a2 + b2 = c2 16. Yes, it is a right triangle because a2 + b2 = c2 17. No, it is not a right triangle because a2 + b2 ≠ c2 18. Yes, it is a triple because a2 + b2 = c2 19. No, it is not a triple because a2 + b2 ≠ c2 20. Yes, it is a triple because a2 + b2 = c2**21. x = 24.8**22. x = 82 23. x = 5.2 24. x = 21.6 25. x = 51 26. x = 17.6**Pythagorean Theorem Mini-project Project**Part One is complete! Create 5 original application problems Labeled diagram Solution with complete sentences Due: Wednesday – beginning of class

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