Chapter 9

Question 1

Theorem 9.1

Answer 1

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

Question 2

Theorem 9.2

Answer 2

In a right triangle the length of the altitude from the right angle to the hypotenuse is the geometric mean of the lengths of the two segments of the hypotenuse.

Question 3

Theorem 9.3

Answer 3

In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. Each leg of the right triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.

Question 4

The Pythagorean Theorem

Answer 4

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

Question 5

Pythagorean Triple

Answer 5

A set of 3 positive integers that satisfy the equation a^2+b^2=c^2

Question 6

Converse of the Pythagorean Theorem

Answer 6

If the square of the lengths of the longest side of a triangle is equal to the sum of the squares of the lengths of the shorter sides, then the triangle is a right triangle,

Question 7

Theorem 9.6

Answer 7

If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the two shorter sides, then the triangle is acute.

Question 8

Theorem 9.7

Answer 8

If the square of the lengths of the longest side of a triangle is greater than the sum of the squares of the lengths of the two shorter sides, then the triangle is obtuse.