Right Triangle Similarity Assignment

In a proof of the Pythagorean theorem using similarity, what allows you to state that the triangles are similar in order to write the true proportions c/a=a/f and c/b=b/e ?

the right triangle altitude theorem

What is the value of x and the length of segment DE? 1. 5/9 = 9/2x+3 2. 10x+15=9(9) x = Length of DE=

6.6 16.2

What is the value of a?

A

What are two different ways you could find the value of a? Explain these methods.

You could use the Pythagorean theorem, since you know the length of the hypotenuse is 9 + 16 = 25 units and the length of one leg is 15 units. To find the value of a, use the relationship that the the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. You could also use the geometric mean (leg) theorem, which states that the length of the hypotenuse is to the length of an adjacent leg as that adjacent leg length is to the length of its corresponding segment in the hypotenuse. So you could write and solve the proportion 25/a = a/6.

What is the value of k?

2

Which similarity statements are true? Check all that apply.

1,4,5 △JKL ~ △KML △JMK ~ △JKL △JMK ~ △KML

What is the value of s?

17

The sides of an equilateral triangle are 8 units long. What is the length of the altitude of the triangle?

B

What is the length of side TS?

B

What is the value of q?

B