Download c2 = a2 + b2

Math 8 Lesson: Pythagorean Theorem Name____________________________________ Block____ Date____________________________ Pythagorean Theorem
c2 = a2 + b2
You Try – Find the missing side:
1.
2.
5 cm
12 cm
15 cm
12 cm
3.
14 cm
x
2.
c
12 ft
10 cm
5. A painter places a 20-foot ladder against a house so that
the base of the ladder is 4 feet from the house. About how
high does the ladder reach on the side of the house?
16 ft
Using Pythagorean Theorem to prove a triangle is a RIGHT triangle
Substitute all three side lengths of a given triangle into
c 2  a2  b2 .
If you get a TRUE STATEMENT (same number on each side of the =), then the triangle IS a right triangle.
Here’s how to substitute:
c 2  a2  b2
Examples:
The measures of three sides of a triangle are given. Is it a right triangle?
a) 9 m, 12 m, 15 m
b)
6 in, 7 in, 12 in
You Try……….. Are the triangles with the given side lengths right triangles?
6. Lengths: 15, 36, 39
7. Lengths: 16, 21, 42
8.
12
9
15
Math 8
The Pythagorean Theorem
Name ________________________
Date: _____________ Block: ____
Write an equation you could use to find the length of the missing side of each right triangle. Then find the missing length. Round to the nearest tenth if necessary. 7. a = 1, b = 3 10. a = 5 yd, b = 11 yd 8. b = 4 ft, c = 7 ft 9. a = 10 yd, c = 18 yd
11. b = 22 m, c = 25 m 12. a = 36 km, c = 60 km Determine whether each triangle with sides of given lengths is a right triangle. 13. 10 yd, 15 yd, 20 yd 14. 21 ft, 28 ft, 35 ft 15. 7 cm, 14 cm, 16 cm 16. The hypotenuse of a right triangle is 15 inches, and one of its legs is 11 inches. Find the length of the other leg. 18. What is the perimeter of a right triangle if the hypotenuse is 15 centimeters and one of the legs is 9 centimeters? 17. The diagonal of a 27‐inch television measures 27 inches. If the width of a 27‐inch is 22 inches, calculate its height to the nearest inch.
19. Tina measures the distances between three cities on a map. The distances between the three cities are 45 miles, 56 miles, and 72 miles. Do the positions of the three cities form a right triangle? Find the two consecutive whole numbers between which the square root of a given number lies. √57 _______ _______ √111 _______ _______ √500 _______ _______ √7 _______ _______ √31 _______ _______ √1000 _______ _______ Estimate each square root to the nearest tenth. Then graph the square root on a number line. 4. √2 5. √10 6.
√73