8th Honors
Name:
Chapter 5-6 Review
Period:
Perform the indicated operation.
1.
2.
3.
4.
Use Pythagorean’s Theorem to find the length of the missing side of the triangle.
5.
7.
6.
A 12-foot ladder is set up 5 feet from the base of a building. How far up the building does the
ladder reach? Round your answer to the nearest tenth of a foot.
8.
Use the converse of the Pythagorean Theorem to determine if the triangle is a right triangle.
Explain your answer.
9.
Determine the distance between (3, 1) and (5, 6) by graphing and connecting the points,
creating a right triangle, and applying the Pythagorean Theorem.
10.
Rectangle ABCD has a length of 18 centimeters and a width of 10 centimeters. What is the
length of diagonal AC?
11.
A rectangular box has a length of 12 inches and a width of 4 inches. The length of the three-
dimensional diagonal of the box is 14 inches. What is the height of the box?
Convert the fraction to a decimal by dividing the numerator by the denominator. Use bar
notation to write repeating decimals.
12.
13.
Write the fraction that represents the repeating decimal.
14.
0.5454
15.
0.4848
Determine if the square root is a rational or irrational number. Explain your reasoning.
16.
17.
Tell whether the statement is true or false.
19.
The set of integers contains the set of rational numbers.
20.
Every repeating decimal is a rational number.
18.
21.
Every square root is an irrational number.
22.
The set of natural numbers contains the set of integers.
23.
Zero is an integer.
24.
A square root is sometimes a rational number.
25.
The set of real numbers is closed under addition.
26.
The set of whole numbers is closed under subtraction.
Identify the property that is illustrated.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
If
, then
If
and
.
, then
The side lengths of a right triangle are 10, 24, and 26. Determine which is the length of the
hypotenuse. Explain your reasoning.
Write an equation to determine the unknown side. Then, solve the equation. Simplify your
answer.
40.
41.
Determine whether the given side lengths form a right triangle.
42.
.
5, 8, 17
43.
16, 30, 34
44.
Rick purchased a rectangular computer monitor that measures 16 inches
tall by 22 inches wide. He wants to know the diagonal measure of the monitor.
Round your answer to the nearest tenth of an inch.
45.
An 18-foot board is leaning against a wall. It is set 6 feet from the base of the wall. How far
up the wall does the board reach? Round your answer to the nearest tenth of a foot.
Determine the distance between each pair of points by graphing and connecting the points,
creating a right triangle, and applying the Pythagorean Theorem.
49.
(4, 2) and (4, 6)
50.
(7, 3) and (2, 9)
51.
A rectangular box is 12 inches in length, 4 inches in width, and 6 inches in height.
a.
Suppose the three-dimensional diagonal is also the hypotenuse of a
right triangle. If a vertical edge is one of the legs of that right triangle,
what is the length of the second leg?
b.
Determine the length of the three-dimensional diagonal.
c.
Use the formula
to calculate the length of the three-dimensional diagonal.