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# 11.5 Special Right Triangls

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Chapter 11, Section 5: Special Right Triangles. 45-45-90 and 30-60-90 Triangles.

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### 11.5 Special Right Triangls

1. 1. Warm Up: Find the missing angle measurements Missing Angle Right Angle 18° The angles of ALL triangles add up to 180 degrees 54° Missing Angle Right Angle
2. 2. Special Right Triangles Chapter 11 Section 5
3. 3. Multiplying Square Roots For nonnegative numbers, the square root of a product equals the product of the square roots. This is how you determine answers not on page 746. √18 = √9 ∙ 2 = √9 ∙ √2 = 3 ∙ √2
4. 4. 45°-45°-90° Triangles Isosceles Right Triangles also known as: 45°-45°-90° triangles. Use the degrees to identify these types of triangles.
5. 5. C² = A² How 45-45-90 Triangles Work + B² ← Pythagorean Theorem *Isosceles triangles have two equal length legs.* Th e r e f o r e , A a n d B a r e t h e s a m e le n g t h ! C² = 2x² ← the length of the leg is now represented by x. C = √2x² ← Undo the square on the c. C = √2 ∙ √x² ← Multiplying Square Roots. C = √2 ∙ x ← The hypotenuse of a 45-45-90 triangle is always √ multiplied by the length of 2 the leg.
6. 6. 45-45-90 Triangles 45° 45-45-90 triangles Hypotenuse = leg x √2 X have congruent leg lengths and the Isosceles hypotenuse is the Right length of the leg Triangle multiplied by √2. 90° X 45°
7. 7. What is the Square Root of 2? √ = 1.41423562 2 So round answers to the nearest tenth unless asked to do otherwise.
8. 8. 30°-60°-90° Triangles Two 30°-60°-90° triangles are formed when you cut an Equilateral Triangle in half. The Hypotenuse of each 30-60-90 is twice the length of the shorter leg. Use Pythagorean Theorem to find the length of the longer leg.
9. 9. 30°-60°-90°: Determ Long Leg ine C² = A² + B² (2x)² = x² + B² ← B is the length of the long leg. 4x² = x² + B² 3x² = B² ← Minus x² √3x² = B ← Undo square root √3 ∙ x = B ← Multiply square root The length of the longer leg = the √ ∙ the 3 length of the shorter leg.
10. 10. Assignment #35: Handout
11. 11. Cool Website On Triangles http://www.800score.com/content/guide7b2.htm l