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Tuesday, October 8 th

Tuesday, October 8 th. Warm Up. Simplify A=8 B=4 C=?. Answers to Homework. A²+B²=C². Pythagorean Triples. IT’S A WAY TO SAVE TIME!!!! 3-4-5 5-12-13. 3-4-5. Example: Multiple of 2: 6-8-10 Mutiple of 3: 9 – 16- 15. Finding Missing Side length. A = 300 B=400 C=? C=500.

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Tuesday, October 8 th

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  1. Tuesday, October 8th Warm Up Simplify A=8 B=4 C=?

  2. Answers to Homework A²+B²=C²

  3. Pythagorean Triples IT’S A WAY TO SAVE TIME!!!! 3-4-5 5-12-13

  4. 3-4-5 Example: Multiple of 2: 6-8-10 Mutiple of 3: 9 – 16- 15

  5. Finding Missing Side length A = 300 B=400 C=? C=500

  6. Today’s Essential Skill Rationalize the Denominator -You can’t leave a square root in the denominator -So, you will multiply numerator and denominator by √3

  7. You Try! Rationalize the denominator 1. 2. 3.

  8. Special Right Triangles You will be able to find the lengths of sides of special right triangles 30-60-90 And 45-45-90

  9. 45-45-90

  10. A 45°-45°-90° triangle is one type of special right triangle. You can use the Pythagorean Theorem to find a relationship among the side lengths of a 45°-45°-90° triangle.

  11. Special Right Triangles Leg:Leg:Hypotenuse

  12. We will use a reference triangle to set up a proportion then solve. In a 45-45-90 triangle… LEGS ARE THE SAME LENGTH

  13. 45-45-90 Right Triangle 1 1 This is our reference triangle for the 45-45-90. Why? 1²+ 1²=C² 1 + 1 = c² 2=c² = √2=c

  14. 45-45-90 Right Triangle x x

  15. Type 1: Finding Hypotenuse Multiply the side length by √2

  16. Just Watch Find the value of x. Give your answer in simplest radical form. By the Triangle Sum Theorem, the measure of the third angle in the triangle is 45°. So it is a 45°-45°-90° triangle with a leg length of 8.

  17. #1 You Try! 45 a√2 x a 3 a 3

  18. #2 x a√2 a 5 a 5

  19. #3 x √7 y Y=The same so √7 X= √7•√2=√14

  20. Type 2: Finding a Leg

  21. Just Watch Type 2 45 3√2 x X=3

  22. You Try Type 2 45 6√2 x X=6

  23. A little Harder….Just Watch Find the value of x. Give your answer in simplest radical form. The triangle is an isosceles right triangle, which is a 45°-45°-90° triangle. The length of the hypotenuse is 5. Rationalize the denominator.

  24. #1 You Try! Type 2 45 3 x 3=x√2

  25. Type 2 #2 18=x√2

  26. y y 8 x x Solve for x and y

  27. y x x 22 #3 and #4 Solve for x

  28. Classwork/Homework 45-45-90 Special right triangles CW: 1-6 HW: on back 1-12

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