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Bell Ringer

Bell Ringer. A right triangle with angles measure of 45,45, and 90 are called 45-45-90 triangles. Example 1. Find the length x of the hypotenuse in the 45° –45° –90° triangle shown at the right. SOLUTION. By the 45° –45° –90° Triangle Theorem, the length of the

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Bell Ringer

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  1. Bell Ringer

  2. A right triangle with angles measure of 45,45, and 90 are called 45-45-90 triangles

  3. Example 1 Find the length x of the hypotenuse in the 45° –45° –90° triangle shown at the right. SOLUTION By the 45° –45° –90° Triangle Theorem, the length of the hypotenuse is the length of a leg times . hypotenuse=leg · 45° –45° –90° Triangle Theorem · = 3 Substitute. 2 2 2 2 The length of the hypotenuse is 3 . ANSWER Find Hypotenuse Length

  4. Example 2 Find the length x of each leg in the 45° –45° –90° triangle shown at the right. SOLUTION By the 45° –45° –90° Triangle Theorem, the length of the hypotenuse is the length of a leg times . hypotenuse= leg · 45° –45° –90° Triangle Theorem 7 = x Substitute. 7 x = Divide each side by . 2 2 2 2 2 2 2 2 7 = x Simplify. 2 The length of each leg is 7. ANSWER Find Leg Length

  5. Find Hypotenuse and Leg Lengths Now You Try  1. 4 ANSWER 3. 2 5 ANSWER 2. 3 ANSWER 2 4. 6 ANSWER Find the value of x.

  6. Example 3 Determine whether there is enough information to conclude that the triangle is a 45° –45° –90° triangle. Explain your reasoning. SOLUTION By the Triangle Sum Theorem, x° + x° + 90° = 180°. Since the measure of each acute angle is 45°, the triangle is a 45° –45° –90° triangle. ANSWER Identify 45° –45° –90° Triangles So,2x° = 90°, andx = 45.

  7. Example 4 Show that the triangle is a 45° –45° –90° triangle. Then find the value of x. SOLUTION The triangle is an isosceles right triangle. By the Base Angles Theorem, its acute angles are congruent. From the result of Example3, this triangle must be a45° –45° –90° triangle. 2 2 hypotenuse= leg · 45° –45° –90° Triangle Theorem 5 = x Substitute. Find Leg Length You can use the 45° –45° –90° Triangle Theorem to find the value of x.

  8. Example 4 5 x Divide each side by . = 5 = x Simplify. 2 2 2 2 2 Use a calculator to approximate. 3.5 ≈ x Find Leg Length

  9. Now You Try  5. The triangle is an isosceles right triangle. By the Base Angles Theorem, its acute angles are congruent. From the result of Example 3, the triangle is a ANSWER 2 8 45° –45° –90° triangle. x = ≈ 5.7. Find Leg Lengths Show that the triangle is a 45° –45° –90° triangle. Then find the value of x. Round your answer to the nearest tenth.

  10. Checkpoint Show that the triangle is a 45° –45° –90° triangle. Then find the value of x. Round your answer to the nearest tenth. 6. The triangle has congruent acute angles. By Example 3, the triangle is a 45° –45° –90° ANSWER 2 12 triangle. x = ≈ 8.5. Now You Try  Find Leg Lengths

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