Test Review (8.1 – 8.3)
8-1: Geometric Mean
Name: _____________________________
Geometric Mean The geometric mean between two numbers is the positive square root of their product.
If x is the geometric mean between a and b, then x =
.
Find the geometric mean between each pair of numbers.
1. 4 and 4
2. 4 and 6
3. 6 and 9
4. and 2
5. 12 and 20
6. 4 and 25
In a right triangle, the altitude is the geometric mean between the two segments of the hypotenuse.
In a right triangle, each leg is the geometric mean between the hypotenuse and the segment of the
hypotenuse adjacent to that leg.
Find x, y, and z to the nearest tenth.
7.
8.
9.
8-2 Study Guide and Intervention
The Pythagorean Theorem and Its Converse
△ABC is a right triangle, so
+
=
.
If the three whole numbers a, b, and c satisfy the equation
and c form a Pythagorean triple.
+
=
, then the numbers a, b,
Find x.
10.
13.
11.
Use a Pythagorean Triple to find x.
14.
12.
You can also use the lengths of sides to classify a triangle.
if
+
then △ABC is a right triangle.
if
+
then △ABC is acute.
If
+
then △ABC is obtuse.
Determine whether each set of measures can be the measures of the sides of a triangle. If so, classify the triangle as
acute, obtuse, or right. Justify your answer.
15. 30, 40, 50
16. 20, 30, 40
17. 18, 24, 30
18. 6, 8, 9
19. 6, 12, 18
20. 10, 15, 20
8-3 Study Guide and Intervention
Special Right Triangles
Properties of 45°-45°-90° Triangles The sides of a 45°-45°-90° right triangle have a
special relationship.
l = length of leg
l
l
l
Find x.
21.
22.
23.
45◦
24.
25.
45◦
45◦
x
26.
5
Properties of 30°-60°-90° Triangles The sides of a 30°-60°-90° right triangle also have a
special relationship.
s = length of small leg
Find x and y.
27.
28.
29.
30.
31.
32.
2s
s