Chapter 9 Test

Question 0

Geometric Mean (Altitude) Theorem

Answer 0

If the altitude is drawn to the hypotenuse of a right triangle, then its length is the geometric mean of the lengths of segments in the hypotenuse.
x/h=h/y
h^2=xy

Question 1

Theorem #1

Answer 1

If an altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the given right triangle and to each other.

Question 2

Geometric mean leg theorem

Answer 2

If the altitude divides the hypotenuse of a right triangle into two segments, then either leg is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to it.

Question 3

Pythagorean Theorem

Answer 3

The square of the measure of the hypotenuse of a right triangle is equal to the sum of the squares of the measures of its legs.

a^2+b^2=c^2

Question 4

Converse of Pythagorean Theorem

Answer 4

If a^2+b^2=c^2, the the triangle is right and the angle opposite the longest side is a right angle.

Question 5

Collary of Pythagorean Theorem

Answer 5

a^2+b^2>c^2 ACUTE

a^2+b^2<c^2 OBTUSE

Question 6

What properties of a rhombus should you know for a rhombus-diagonal problem?

Answer 6

• All sides are congruent
• Diagonals are perp bisectors of each other
• Diagonals form 4 congruent right isosceles triangles