CPGeometry 3/19/13
Geometric Mean, Pythagorean Inequality Practice
Name______________________________________
1a.
Sketch the three similar right triangles pictured
b.
Write a similarity statement to identify the 3 similar triangles.
2a.
Explain how to find the geometric mean of two numbers.
b.
Calculate the geometric mean of 18 and 6. Show all work.
c.
Find the geometric mean of each pair of numbers
5 3
4 12
and
9
7

d.



Circle the equation represents the statement “ x is the geometric mean of y and z”?
x

3 2
5 2
and
5
9
yz
2
x  yz

x  yz

3.
Solve for x. Show all work.
4.
Solve for x, y and z. Show work to support your answer.
5.
Solve for x, y and z. Show work to support your answer.
6.
Determine whether each set of numbers can be the measures of the sides of a triangle. Explain.
a.
7.
8.
4, 8, 12
b.
12, 4, 15
c.
6, 7,11
Given the lengths of two sides of a triangle, write an inequality to show the possible lengths of the
third side.
a.
5, 13
b.
22, 8
c.
3, 5
d.
1, 16
e.
19, 4
f.
36, 17
Given the measures of three sides of a triangle, classify the triangle as acute, obtuse or right.
Justify your answer.
a.
6, 7, 3 13
b.
8, 10, 6
d.
3, 9, 10

c.

2 8,
162 , 3 32
p. 553 # 30-32
Classify XYZ as acute, obtuse or right. Justify your answer using the Pythagorean Inequality Theorems.
Show all work.
30.

X (-3, -2), Y(-1,0), Z (0, -1)
31.
X ( -7, -3), Y (-2, -5) , Z (-4, -1)
32.
X (1, 2), Y (4, 6), Z (6, 6)