Ch 9 Worksheet Key
Name ___________________________
Worksheets Chapter 9: The Pythagorean theorem
Warm Up:
Find the area of an isosceles triangle with a leg measure of 10 cm and a base measure of 16 cm.
c2  a 2  b2
10
10
6
102  82  h 2
100  64  h
16
2
h 2  36
h  36  6
1
16  6 
2
A  48 cm 2
A
Note: You can’t do this unless you have a way to find the height.
EXERCISES Lesson 9.1 Page 481 #1 – 10, 12, 14, 16.
Show how you are finding your answers! You MUST use the procedure described in the notes. If you
need to approximate, round your answers to 3 decimal places. You will need your book for #12, 14 & 16.
c  a b
2
2
c  12  15
2
2
a  12
2
82  6 2  b 2
2
64  36  b 2
c  144  225
2
28  b 2
c  369
2
b  28  5.292
c  369  19.209
d  10
S. Stirling
c2  a 2  b2
s  676  26
c  72  8.485
Page 1 of 6
Ch 9 Worksheet Key
b  576  24
Name ___________________________
c2  a 2  b2
3.92  1.52  x 2
x  1600  40
15.21  2.25  x 2
12.96  x 2
x  12.96  3.6
12. Baseball infield a square. What is the distance from home plate
to second base?
s  16200  127.279 ft
90
x
c  a b
2
2
5 s s
2
2
2
d
2
90
25  2 s 2
x
12.5  s 2
s  12.5  3.536
14. Length of diagonal of a square whose area
is 64 cm2.
d  128  11.314 cm
S. Stirling
16. Side rectangular garden 6 m and diagonal 10 m. Find
perimeter.
p  28 m
Page 2 of 6
Ch 9 Worksheet Key
Name ___________________________
9.2 The Converse of the Pythagorean Theorem
Investigation:
Use the three given sides, classify the triangle as acute, right or obtuse. (Or it may not make a triangle at
all.) You may want to use a compass and a ruler in your investigation. All measures are in centimeters.
Triangle 1: 2, 3, 5 Not a triangle
Triangle 2: 3, 4, 5 Right triangle
Triangle 3: 2, 4, 5 Obtuse triangle
Triangle 4: 6, 8, 10 Right triangle
Triangle 5: 7, 8, 10 Acute triangle
Triangle 6: 9, 12, 15 Right triangle
Compare the lengths of the sides of the right triangles. Is there any relationship you can find?
The sides of triangle 4 and 6 are in the same ratio as triangle 2.
S. Stirling
Page 3 of 6
Ch 9 Worksheet Key
Name ___________________________
EXERCISES Lesson 9.2 Page 486-487 #1 – 8, 11, 13, 15
Show how you are finding your answers! You MUST use the procedure described in the notes. If you
need to approximate, round your answers to 3 decimal places. You will need your book for directions.
c  a b
2
2
2
It’s a right triangle.
It’s NOT a right triangle.
17 2  82  152
289  64  225
289  289
So it’s a right triangle.
OR say it’s a 8: 15: 17
Pythagorean Triple
It’s NOT a right triangle.
It’s NOT a right triangle.
c2  a 2  b2
2.232  1.732  1.412
4.9729  2.9929  1.9881
4.9729  4.981
So it’s NOT a right triangle.
7.
8.
It’s NOT a right triangle.
It’s NOT a right triangle. And the window frame is
not a rectangle.
S. Stirling
Page 4 of 6
Ch 9 Worksheet Key
11.
Name ___________________________
The height of the cylinder is 17.349 m.
13. Hypotenuse = 17 cm; one leg = 15 cm. Find area of the right triangle.
A  60 cm 2
15. Congruent sides of an isosceles triangle measures 6 cm and the base
measures 8 cm. Find the area.
c2  a 2  b2
62  42  h 2
36  16  h 2
20  h 2
h  20  4.472 cm
S. Stirling
1
bh
2
1
A   8  4.472
2
A  17.888 cm 2
A
Page 5 of 6
Ch 9 Worksheet Key
Name ___________________________
EXTRA EXERCISES Chapter 9
1. If the leg of a right isosceles triangle measures 6
feet, how long is its hypotenuse?
h  72  8.485
5. Find the area of an equilateral triangle with side
length 10 m.
7
A  43.3 m 2
2. Find the area of an isosceles triangle with a base
of 16 and legs measuring 17 inches.
A  120 in 2
6. If the hypotenuse of a right isosceles triangle
measures 24 feet, what is its area?
A  144.007 m 2
3. The sides of a rhombus measure 10 in. and the
shorter diagonal measures 12 in, what is the area
of the rhombus? Hint: use right triangles.
A  96 in 2
7. If the diagonal of a square measures 10 m, what is
its area?
A  49.999 ft 2
4. Find the area of an equilateral triangle with side
length 16 m.
A  110.848 m 2
8. If the diagonal of a rectangle measures 25 m and
the height measures 7 m, what is its perimeter?
Explain fully!
S. Stirling
p  62 m
Page 6 of 6