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Warm Up for Section 1.1 Simplify: (1). (2).

x o. c. a. 40 o. b. Warm Up for Section 1.1 Simplify: (1). (2). Use the triangle below to answer #3, #4: (3). Find x. (4). If a = 5, b = 3, find c. x o. c. a. 40 o. b. Answers for Warm Up, Section 1.1

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Warm Up for Section 1.1 Simplify: (1). (2).

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  1. xo c a 40o b Warm Up for Section 1.1 Simplify: (1). (2). Use the triangle below to answer #3, #4: (3). Find x. (4). If a = 5, b = 3, find c.

  2. xo c a 40o b Answers for Warm Up, Section 1.1 Simplify: (1). (2). Use the triangle below to answer #3, #4: (3). Find x. (4). If a = 5, b = 3, find c.

  3. Work for Answers to WU, Section 1.1 (1). (2). (3). x = 90 – 40 (4). a2 + b2 = c2 = 50 52 + 32 = c2 25 + 9 = c2 34 = c2 = c

  4. Special Right Triangles Standard: MM2G1a, b Essential Question:What is the relationship between the lengths of the legs of a 45°–45°–90°triangle and a 30°–60°–90°triangle? Section 1.1

  5. Vocabulary Right Triangle: A triangle containing one angle that measures exactly 90 degrees. Hypotenuse: The longest side of a right triangle. Reference angle: The measured, or known angle in a right triangle other than the 90° angle.

  6. Investigation 1: With your partner, complete each step in the investigation then answer questions 1-10. Step 1: Using the grid paper provided and a straightedge, draw a square with side length 5 cm. Step 2: Label the vertices of the square A, B, C, and D. Label each side with its length. Step 3: Using a straightedge, draw diagonal .

  7. Investigation 1: A 5 cm B 5 cm 5 cm D C 5 cm

  8. Answer the following questions: (1). mD = ____o(2). mACD = ____o (3). mDAC = ____o (4). DC = ____ (5). AD = ____ (6). ADC is (acute, right, obtuse). (7). ADC is (isosceles, scalene, equilateral). (8). Using the Pythagorean Theorem, find AC. Be sure to write your answer in simple radical form. 90 45 5 cm 45 5 cm

  9. a2 + b2 = c2 52 + 52 = x2 45° 25 + 25 = x2 50 = x2 5 x 45° 5

  10. Look at two additional 45o-45o-90o triangles and determine the length of the hypotenuse, x. Be sure to write your answer in simple radical form.

  11. Question 9: Find x a2 + b2 = c2 32 + 32 = x2 45° 9 + 9 = x2 18 = x2 x 3 45° 3

  12. Question 10: Find x a2 + b2 = c2 82 + 82 = x2 45° 64 + 64 = x2 128 = x2 x 8 45° 8

  13. Summary: In a 45o-45o-90o triangle (a). Length of hypotenuse = length of leg times . (b). Length of legs = length of hypotenuse divided by . 45° x 45° x

  14. Investigation 2: With your partner, complete the following regarding equilateralABC where AB =10: Step 1: Label the length of each edge. Step 2: Label the measure of B and C. Step 3: Using a straightedge, draw and label altitude . Step 4: Label the length of and . Step 5: Label the measure of BAD and CAD. Step 6: Label the measure of ADC. Step 7: Using the Pythagorean Theorem, find AD.

  15. a2 + b2 = c2 A 52 + x2 = 102 25 + x2 = 100 75 = x2 30° 30° 10 10 x 60° 60° B C 5 5 D 10

  16. Investigation 2: Note: the two legs of a 30o-60o-90o triangle are NOT equal in measure. The longer leg will always be opposite the ___o angle. The shorter leg will always be opposite the ___o angle. 60 30

  17. R 30° RT ST 12 60° S T 6 Consider the 30o-60o-90o right triangle created from an equilateral triangle pictured at right. (13). The long leg is segment ______ and the short leg is segment _______. (14). Use the Pythagorean Theorem to find RT.

  18. a2 + b2 = c2 62 + x2 = 122 R 36 + x2 = 144 108 = x2 30° 12 60° S T 6

  19. 30° 2x 60° x Summary: In a 30o-60o-90o triangle: Length of hypotenuse = length of short leg times 2 Length of long leg: length of short leg times Length of short leg: half the length of hypotenuse or the length of the long leg divided by

  20. Check for Understanding: Find the missing edge lengths for each triangle: Example 13:

  21. 60o 30o Check for Understanding: Find the missing edge lengths for each triangle: Example 14:

  22. Check for Understanding: Find the missing edge lengths for each triangle: Example 15:

  23. 60o 30o Check for Understanding: Find the missing edge lengths for each triangle: Example 14:

  24. 60o 30o Check for Understanding: Find the missing edge lengths for each triangle: Example 14:

  25. 60o 30o Check for Understanding: Find the missing edge lengths for each triangle: Example 14:

  26. 60o 30o Check for Understanding: Find the missing edge lengths for each triangle: Example 14:

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