# 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. 40 o a b c xoxo.

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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. 40 o a b c xoxo

Work for Answers to WU, Section 1.1 (1). (2). (3). x = 90 – 40 (4). a 2 + b 2 = c 2 = 50 5 2 + 3 2 = c 2 25 + 9 = c 2 34 = c 2 = c

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

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.

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.

Investigation 1: A B CD 5 cm C

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 5 a 2 + b 2 = c 2 5 2 + 5 2 = x 2 25 + 25 = x 2 50 = x 2 x

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

45° 3 3 a 2 + b 2 = c 2 3 2 + 3 2 = x 2 9 + 9 = x 2 18 = x 2 x Question 9: Find x

45° 8 8 a 2 + b 2 = c 2 8 2 + 8 2 = x 2 64 + 64 = x 2 128 = x 2 x Question 10: Find x

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

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

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

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

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

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