Chapter 7- Pythagorean

Question 1

Pythagorean theorem

Answer 1

In a right triangle, the hypotenuse squared is equal to the sum of the legs squared

Question 2

3 converse theorems to pythagorean

Answer 2

1. If c squared=a(squared) + b(squared), then it is a right triangle
2. If c(squared)> then it is obtuse
3. If c(squared)< then it is acute

Question 3

What are the 4 pythagorean triples?

Answer 3

1. 3, 4, 5
2. 5, 12, 13
3. 8, 15, 17
4. 7, 24, 25

Question 4

Altitude triangle similarity theorem

Answer 4

If the altitude is drawn to the hypotenuse of a right triangle, then the triangles are similar.

Question 5

Altitude geometric mean theorem

Answer 5

The length of the altitude is the geometric mean of the lengths of the two segments of the hypotenuse

Question 6

Leg geometric mean theorem

Answer 6

The length of each leg of a right triangle is the geometric mean of the total length of the hypotenuse and the side of the hypotenuse closest to it

Question 7

Ratios for a 45. 45. 90 triangle? 30, 60, 90?

Answer 7

1: 1:Square root of 2
1: square root of 3, 2

Question 8

What is the sin ratio? Cos? Tan?

Answer 8

Sin- opposite/hypotenuse

Cos-adjacent/hypotenuse

Tan-opposite/adjacent