13 3 Special Right Triangles p 709 CCSS

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13. 3 Special Right Triangles p 709 CCSS – SRT 8. 1 Derive and

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

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

answers • An isosceles triangle has at least 2 congruent sides. • Two angles whose measures have a sum of 90 o. • 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

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 +

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

 • Use the Pythagorean Theorem to find the length of the hypotenuse in

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

answer • AB 2 = x 2 + x 2 • AB 2 =

answer • AB 2 = x 2 + x 2 • AB 2 = 2 x 2 • AB = x√ 2

Reflections • 1. Is it true that if you know one side length of

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

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

• 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

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

 • 2. A student has drawn a right triangle with a 60 o

• 2. A student has drawn a right triangle with a 60 o 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.