13.3 Special Right Triangles p 709

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Presentation transcript:

13.3 Special Right Triangles p 709 CCSS – SRT 8.1 Derive and use the trigonometric ratios for special right triangles

Warm up What is an isosceles triangle? What do you mean by complementary angles? What is an Isosceles Triangle Theorem What is the Pythagorean Theorem?

answers An isosceles triangle has at least 2 congruent sides. Two angles whose measures have a sum of 90o. If two sides of a triangle are congruent, then the angles opposite the sides are congruent.

Explore 1 Investigating an isosceles Right Triangle Discover relationships that always apply in an isosceles right triangle. A. Draw an isosceles right triangle ABC with legs measures x and right angle at C. Identify the base angles, and use the fact that they are complementary to write an equation relating their measures. B. Use the Isosceles Triangle Theorem to write a different equation relating the base angle measures. C. What must the measures of the base angles be? Why?

answers A. Base angles are / A and /B m/ A + m /B = 90o B. m/ A = m /B C. 45o

Use the Pythagorean Theorem to find the length of the hypotenuse in terms of the length of each leg, x.

answer AB2 = x2 + x2 AB2 = 2x2 AB = x√2

Reflections 1. Is it true that if you know one side length of an isosceles right triangle, then you know all the side lengths? Explain. 2. Suppose you draw the perpendicular from C to AB. Explain how to find the length of CD.

Explore 2 : Investigating another special right triangle Discover relationships that always apply in a right triangle formed as half of an equilateral triangle.

ΔABD is an equilateral triangle and BC is a perpendicular from B to AD ΔABD is an equilateral triangle and BC is a perpendicular from B to AD. Determine all three angle measures in ΔABC.

Reflections 1. What is the numerical ratio of the side lengths in a right triangle with acute angles that measure 30o and 60o? Explain.

2. A student has drawn a right triangle with a 60o angle and a hypotenuse of 6. He has labeled the other side lengths as shown. Explain how you can tell at a glance that he has made an error and how to correct it.