5.4 What If The Triangle Is Equilateral? Pg. 9 Equilateral Triangles

5.4 – 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.

5.17 – 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. Do you see any patterns? Look for a relationship between the sides of the triangle and the height. The hypotenuse is always double the bottom The height is the bottom times the

e. 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.

f. 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.

5.19 – 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.

5.20 – 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? 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

5.21 – SPECIAL TRIANGLE RATIOS Write in the ratios of the sides for the given special triangles.

3.10

5.22 – WORKING TRIANGLE IN KITCHEN In the traditional kitchen the three main work sites are the refrigerator, the sink, and the stove. These represent the three points of the kitchen work triangle. If you place these too far away from each other you waste a lot of steps while preparing a meal. If they are too close to each other you have a cramped kitchen with out any place to work.

Each side of the triangle should be between 4 and 9 feet The total of all three legs should be between 12 and 26 feet No obstructions should be in the work triangle

a. What is d, the distance, in feet, along the side of the Work Triangle from the sink (S) to the refrigerator (R)? Show or explain how you got your answer.

b. What is h, the height, in feet, of the Work Triangle? Show or explain how you got your answer.

c. What is x, the distance, in feet, along the side of the Work Triangle from the sink (S) to the oven? Show or explain how you got your answer.

d. Based on this information, is this a good working triangle for a kitchen?

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