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Study Guide and Review
Choose the term that best matches the statement or phrase.
1. a square of a whole number
SOLUTION: A perfect square is a square of a whole number.
ANSWER: perfect square
2. a triangle with no congruent sides
SOLUTION: A scalene triangle has no congruent sides.
ANSWER: scalene
3. decimals that do not repeat or terminate
SOLUTION: Decimals that do not repeat or terminate are called irrational numbers.
ANSWER: irrational numbers
4. the sides of a right triangle that are adjacent to the right angle
SOLUTION: The sides of a right triangle that are adjacent to the right angle are called legs.
ANSWER: legs
5. a triangle with angle measures 73°, 30°, and 77°
SOLUTION: A triangle with angle measures 73°, 30°, and 77° is an example of an acute triangle because all the angles are acute,
or less than 90° and because they all have different measures. It is also an example of a scalene triangle. Since all the angle measures are different, all the sides are different lengths as well.
ANSWER: scalene or acute triangle
6. the side opposite the right angle in a triangle
SOLUTION: The side opposite the right angle is called the hypotenuse.
ANSWER: hypotenuse
7. sides of a figure that have the same length
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Sides of a figure that have the same length are congruent.
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SOLUTION: The side opposite the right angle is called the hypotenuse.
ANSWER: Study
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hypotenuse
7. sides of a figure that have the same length
SOLUTION: Sides of a figure that have the same length are congruent.
ANSWER: congruent
8. the point at which two sides of a triangle intersect
SOLUTION: The vertex is the point at which two sides of a triangle intersect.
ANSWER: vertex
9. used to indicate a positive square root
SOLUTION: A radical sign is used to indicate a positive square root.
ANSWER: radical sign
10. part of a line containing two endpoints and all the points between them
SOLUTION: Part of a line containing two endpoints and all the points between them is called a line segment.
ANSWER: line segment
Find the square root.
12. SOLUTION: = –5
ANSWER: −5
14. SOLUTION: = 22
ANSWER: 22
Estimate the square root to the nearest integer. Do not use a calculator.
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SOLUTION: The first perfect square less than 52 is 49.
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= 7
= 22
ANSWER: Study
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22
Estimate the square root to the nearest integer. Do not use a calculator.
16. SOLUTION: = 7
The first perfect square less than 52 is 49.
= 8
The first perfect square greater than 52 is 64.
The negative square root of 52 is between the integers –7 and –8. Since 54 is closer to 49 than to 64,
to –7 than to –8.
is closer
ANSWER: −7
18. SOLUTION: = 20
The first perfect square less than 415 is 400.
The first perfect square greater than 415 is 441.
= 21
The square root of 415 is between the integers 20 and 21. Since 415 is closer to 400 than to 441,
20 than to 21.
is closer to ANSWER: 20
Name all of the sets of numbers to which the real number belongs. Write whole, integer, rational, or
irrational.
20. 18
SOLUTION: Since 18 =
, this number is a rational number. So, 18 is a whole number, an integer, and a rational number.
ANSWER: whole, integer, rational
22. SOLUTION: cannot be written as a fraction, so it is an irrational number.
ANSWER: irrational
Replace the Ο with <, >, or = to make a true statement.
24. Ο SOLUTION: = 6.2525…
= 6.2449…
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Since
is to the right of ANSWER: ,
> .
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cannot be written as a fraction, so it is an irrational number.
ANSWER: Study
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irrational
Replace the Ο with <, >, or = to make a true statement.
24. Ο SOLUTION: = 6.2525…
= 6.2449…
is to the right of Since
,
> .
ANSWER: > 26. Ο SOLUTION: −11 = –11.1111…
= –11.1355…
Since −11
is to the right of
, −11
>
.
ANSWER: > Solve the equation. Round to the nearest tenth, if necessary.
28. d 2 = 100
SOLUTION: The solutions are 10 and –10.
ANSWER: 10, −10
30. GARDENS The formula A ≈ 3.14r2 can be used to determine the area of a circle where A is the area and r is the
distance from the center of the circle to the outside edge. If the area of a circular garden is 700 square feet, about
how far is the distance from the center of the garden to the outside edge? Round to the nearest tenth.
SOLUTION: To find the distance from the center of the garden to the outside edge, you will need to find the radius of the circle.
2
Substitute 700 for A in the equation A ≈ 3.14r .
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The solutions are 10 and –10.
ANSWER: Study
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10, −10
30. GARDENS The formula A ≈ 3.14r2 can be used to determine the area of a circle where A is the area and r is the
distance from the center of the circle to the outside edge. If the area of a circular garden is 700 square feet, about
how far is the distance from the center of the garden to the outside edge? Round to the nearest tenth.
SOLUTION: To find the distance from the center of the garden to the outside edge, you will need to find the radius of the circle.
2
Substitute 700 for A in the equation A ≈ 3.14r .
Since radius is a positive value, the distance from the center of the garden to the outside edge is about 14.9 feet.
ANSWER: 14.9 ft
Find the value of x in the triangle. Then classify the triangle by its angles and by its sides.
32. SOLUTION: The sum of the measures of the angles of a triangle is 180°.
The measure of the angle is 54°.
Angles: The triangle has all acute angles.
Sides: The triangle has two congruent sides.
The triangle is an acute isosceles triangle.
ANSWER: 54; acute isosceles
34. SOLUTION: The sum of the measures of the angles of a triangle is 180°.
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The measure of the angle is 95°.
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The triangle is an acute isosceles triangle.
ANSWER: Study
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54; Guide
acute isosceles
34. SOLUTION: The sum of the measures of the angles of a triangle is 180°.
The measure of the angle is 95°.
Angles: The triangle has an obtuse angle.
Sides: The triangle has no congruent sides.
The triangle is an obtuse scalene triangle.
ANSWER: 95; obtuse scalene
Find the missing length of the triangle. Round to the nearest tenth, if necessary.
36. SOLUTION: Use the Pythagorean Theorem, substituting 30 for a and 40 for b.
So, the missing length is 50 inches.
ANSWER: 50
38. SOLUTION: Use the Pythagorean Theorem, substituting 7 for a and 20 for c.
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So, the missing length is 50 inches.
ANSWER: Study
50 Guide and Review
38. SOLUTION: Use the Pythagorean Theorem, substituting 7 for a and 20 for c.
So, the missing length is about 21.2 centimeters.
ANSWER: 21.2
40. SOFTBALL On a fast pitch softball diamond, the bases are 60 feet apart. What is the distance from home plate to
second base in a straight line to the nearest tenth of a foot?
SOLUTION: Drawing a straight line from home plate to second base forms a right triangle with legs of 60 feet. Use the
Pythagorean Theorem to find the hypotenuse, which is the distance between home plate and second base.
The distance between home plate and second base is about 84.9 feet.
ANSWER: 84.9 ft
Find the distance between the pair of points. Round to the nearest tenth, if necessary.
42. B(−2, 7), C(−5, 7)
SOLUTION: Use the Distance Formula.
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The distance between home plate and second base is about 84.9 feet.
ANSWER: Study
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84.9 ft
Find the distance between the pair of points. Round to the nearest tenth, if necessary.
42. B(−2, 7), C(−5, 7)
SOLUTION: Use the Distance Formula.
The distance between B and C is 3 units.
ANSWER: 3
44. M (−8, 1), N(7, −6)
SOLUTION: Use the Distance Formula.
The distance between M and N is about 16.6 units.
ANSWER: 16.6
46. LAKES A distance of 2 units on a coordinate plane equals an actual distance of 1 mile. Suppose the locations of
two lakes on a map are at (26, 15) and (9, 20). Find the actual distance between these lakes to the nearest mile.
SOLUTION: Use the Distance Formula to find the distance between the two lakes on the map.
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The distance between M and N is about 16.6 units.
ANSWER: Study
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16.6
46. LAKES A distance of 2 units on a coordinate plane equals an actual distance of 1 mile. Suppose the locations of
two lakes on a map are at (26, 15) and (9, 20). Find the actual distance between these lakes to the nearest mile.
SOLUTION: Use the Distance Formula to find the distance between the two lakes on the map.
The distance between the two lakes on the map is about 17.7 units. Because every 2 units is equal to 1 mile, divide
by 2 to find the actual distance.
17.7 ÷ 2 = 8.85
So, the lakes are about 9 miles apart.
ANSWER: 9 mi
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