5.2 What If The Triangle Is Equilateral? Pg. 6 Equilateral Triangles.

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5.2 What If The Triangle Is Equilateral? Pg. 6 Equilateral Triangles

5.2 – What If The Triangle Is Equilateral? Equilateral Triangles You now know that isosceles right triangles have a special ratio between the sides. Today you are going to explore a relationship in equilateral triangles.

5.5 – EQUILATERAL TRIANGLES What if the shape isn't a square? See if you can find another special relationship with equilateral triangles.

a. Draw an equilateral triangle with a side length of 2in. Then find the height. 2in 1in

b. Draw an equilateral triangle with a side length of 6in. Then find the height. 6in 3in

c. Draw an equilateral triangle with a side length of 8in. Then find the height. 8in 4in

d. Since all equilateral triangles are similar, Nick decided to follow the pattern to find all of the missing lengths the equilateral triangles below, including the height.

e. Nick noticed that when you draw in the height of an equilateral triangle, it makes two equal right triangles. Given this fact, find all of the missing angles in the given picture. Then find the missing sides in respect to x.

If the side opposite the 30° is ______, the side opposite the 60° is ______, and opposite the 90° is ______.

5.7 – SCRAMBLED FUN Use your new 45°-45°-90° and 30°-60°-90° triangle patterns to quickly find the lengths of the missing sides in each of the triangles below. Do not use a calculator. Leave answers in exact form.

5.8 – DOES THIS ALWAYS WORK? Elijah started to solve the given triangle. He decides to use the ratios for the 30°-60°-90° triangle. Is he correct? a. Can he use the pattern for the 30°-60°- 90° triangle? Why or why not? No, Only right angle given

b. Can he use the pattern for the 45°-45°- 90° triangle? Why or why not? No, legs aren’t equal

c. How does Elijah need to solve this triangle, given the two sides? Solve for the missing side. Pythagorean theorem

5.9 – AREA OF EQUILATERAL TRIANGLES Find the area of each equilateral triangle.

5.10 – COMBINING SPECIAL TRIANGLES Find the missing side lengths in the given triangles using special ratios.

Right Triangles Project Pythagorean Theorem: Given 2 sides 45º– 45º– 90º 30º– 60º– 90º Sine – S sin -1, cos -1, tan -1 Your Name Block# Cosine – C Tangent – T OHOH AHAH OAOA Clinometer Measures Area of Regular Polygons

30º– 60º– 90º x 30° 60° 2x 8 30° 60° y x 30° 60° y