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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. Work for Answers to WU, 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. 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

  3. Special Right Triangles Standard: MM2G1a, b Essential Question:What is the relationship between the lengths of the edges in a 45°–45°–90°triangle? Section 1.1

  4. 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.

  5. 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 .

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

  7. 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

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

  9. 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.

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

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

  12. 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

  13. Examples: Find the missing edge lengths. (11). (12). (13). 10 45o 45o 45o 45o 9

  14. (14). If the diagonal of a square measures inches, what is the perimeter of the square? 5 P = 5 + 5 + 5 + 5 = 20 5 The perimeter of the square is 20 inches.

  15. (15). If the area of a square measures 64 square centimeters, what is the length of the diagonal of the square? 8 8 The length of the diagonal is

  16. Formula Sheet: 45° x 45° x Length of hypotenuse = length leg ∙ Length of leg = length of hypotenuse ÷

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