Name:_________________
Date:_____________
Warm Up
1. Let z = 5 and y = 9. Solve for x
x2  y 2  z 2
2. Find the Geometric Mean of 8 and 25
3. Two vehicles, each moving from a point in a straight line away from each other at an
angle, are 150 feet apart after 6 seconds. Both are moving at a constant rate, vehicle A at 50
feet per second and vehicle B at 40 feet per second.
How far apart are they after 15 seconds?
A. 150 ft.
B. 375 ft.
C. 600 ft.
D. 750 ft.
4. Line segments AC and BD intersect at E, as shown in the figure. AB CD , DE = 10,
BE = 15, and CE = 20. What is the measure of AE ?
A. 13
B. 17
C. 25
D. 30
Pythagorean Theorem
Pythagorean Theorem –
Examples
Find the length of the unknown side of the right triangle. Determine whether the unknown side is a leg or
hypotenuse.
8
1.
2.
x
3
6
x
5
3.
4.
x
12
4
9
x
6
5. A 16 foot ladder rests against the side of the house, and the base of the ladder is 4 feet away.
Approximately how high above the ground is the top of the ladder?
6. Find the area of an isosceles triangle with side lengths 10 meters, 13 meters and 13 meters.
Tell whether the given triangle is a right triangle.
8.
9.
22
14
3 34
9
26
15
Tell whether a triangle with the given side lengths is a right triangle.
10. 4, 4 3 , 8
11. 10, 11, and 14
12. 5, 6, and
61
Classifying Triangles
c2 = a2 + b2
also written
a2 + b2= c2
c2 < a2 + b2
also written
a2 + b2 > c2
c2 > a2 + b2
also written
a2 + b2 < c2
13. Can segments with lengths of 4.3 feet, 5.2 feet, and 6.1 feet form a triangle? If so, would the
triangle be acute, right, or obtuse?
14. Show that segments with lengths 3, 4, and 6 can form a triangle and classify the triangle as acute,
right, or obtuse
Geometry
Worksheet – Practice Pythagorean Theorem
Name_______________________________
Find the unknown side length. Simplify answers that are radicals.
1.
2.
12
3.
x
x
19
7
6
13
5
x
Decide whether the numbers can represent the side lengths of a triangle. If they can, classify the
triangle as right, acute, or obtuse.
4. 5, 12, 13
5. 8, 4, 6
6. 20, 21, 28
7. The length of the hypotenuse of a right triangle is 17 centimeters and the length of one leg is 15
centimeters. What is the length of the other leg?
8. The lengths of the legs of a right triangle are 3 and 5. Find the length of the hypotenuse.
9. In the right triangle QRS, mQ  90, RS = 13, and RQ =5. Find QS.
R
Q
S
10. The length of the hypotenuse of a right triangle is 15 and the length of one leg is 3. What is
the length of the other leg?