Caitlin works part-time at the mall
Name _______________________________________ Date __________________ Class __________________ LESSON
8-5
Review for Mastery Classifying Polygons
A polygon is a closed figure that starts and stops at the same point. A polygon is made up of line segments that do not cross. Determine whether each figure is a polygon. If it is not, explain why not. 1.
2.
_______________________
3.
________________________
________________________
Polygons can be classified by the number of sides or angles. The number of sides and angles is the same. Complete the table. Name
Number of Sides
Number of Angles
3
3
4. 5.
Quadrilateral
4
6.
Pentagon
5
7.
Hexagon
8.
Heptagon
6 7
9.
8
10.
Nonagon
11.
Decagon
8
9 10
All the sides of a regular polygon have the same length, and all the angles have the same measure. Determine whether each is a regular polygon. If it is not, explain why not. 12.
13.
_______________________
14.
________________________
________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
44
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________ LESSON
8-6
Review for Mastery Classifying Triangles
All triangles have at least two acute angles. If the third angle is acute, the triangle is an acute triangle.
If the third angle is right, the triangle is a right triangle.
If the third angle is obtuse, the triangle is an obtuse triangle.
A triangle is scalene if each side is a different length.
A triangle is isosceles if two sides are the same length.
A triangle is equilateral if all three sides are the same length.
Use the figure to complete the statements. 1. Each of the 3 angles is less than 90°, so the triangle is an ________________ triangle. 2. The triangle has 3 sides that have the same length, so it is an ________________ triangle. Use the figure to complete the statements. 3. The triangle has a 90° angle, so it is a ________________ triangle.
4. The triangle has 2 sides that have the same length, so it is an ________________ triangle. Use the figure to complete the statements. 5. The triangle has an angle that measures more than 90°, so it is an ________________ triangle. 6. Each side of the triangle has a different length, so it is a ________________ triangle.
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
52
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________ LESSON
8-7
Review for Mastery Classifying Quadrilaterals
Quadrilaterals are polygons that have 4 sides. In the figures below, arrows are used to indicate parallel sides, and tick marks are used to indicate congruent sides. • A trapezoid is a quadrilateral with • A rhombus is a parallelogram with all only one pair of parallel sides. four sides congruent.
• A parallelogram is a quadrilateral with two pairs of parallel sides.
• A square is a rectangle with all four sides congruent.
• A rectangle is a parallelogram with all four angles congruent.
Use the figures to complete the statements. 1. The figure is a __________________ since it has __________________ pair of parallel sides. 2. The figure is a __________________ and a __________________ since it has __________________ pair(s) of parallel sides, and __________________
sides are congruent.
3. The figure is a __________________ and a __________________ and a __________________ and a __________________ since it has __________________
pair(s) of parallel sides,
angles are congruent, and
__________________
__________________
sides are congruent.
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
60
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________ LESSON
8-8
Review for Mastery Angles in Polygons
The sum of the measures of the three angles of any triangle is 180°. To find the missing angle, subtract the sum of the two given angles from 180°. Find the measure of N in triangle LMN. 1. N ______________________ (74° 57°) 2. N ______________________ 131° 3. N ______________________ Find the measure of the unknown angle. 4.
5.
_______________________
6.
________________________
________________________
Use the figures to complete Exercises 7–10. Figure
Number of Sides
7.
Quadrilateral
4
8.
Pentagon
5
9.
Hexagon
6
Number of Triangles
10. The number of triangles is always ___________________ less than the number of sides of the figure. Find the sum of the interior angles. 11.
12.
180° • ______ ______
13.
180° • ______ ______
180° • ______ ______
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
68
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________ LESSON
9-2
Review for Mastery Perimeter and Circumference
The perimeter of any figure is the distance around the figure. Think of perimeter as “going around the rim” of a figure. Find the perimeter of a figure by adding the measures of the sides.
The word perimeter has the word rim in it.
Find the perimeter of each polygon.
P659 P 20
P 7 11 10 8 P 36
The perimeter of the triangle is 20 in.
The perimeter of the quadrilateral is 36 cm.
To find the perimeter of a rectangle, you can add the length and the width and multiply the sum by 2. The formula for the perimeter of a rectangle is P 2( ). P 2( ) P 2(8 5) P 2(13) P 26 The perimeter of the rectangle is 26 feet. Find the perimeter of each polygon. 1.
2.
P _____ _____ _____ P _____ m
3.
P _____ _____ _____ _____
P 2(_____ _____) P _____ cm
P _____ ft
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
16
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________ LESSON
9-2
Review for Mastery Perimeter and Circumference (continued)
The distance around a circle is called the circumference. To find the circumference of a circle, you need to know the diameter or the radius of the circle. C The ratio of the circumference of any circle to its diameter is d always the same. This ratio is known as (pi) and has a value of approximately 3.14. To find the circumference C of a circle if you know the diameter d, multiply times the diameter. C • d, or C 3.14 • d. C•d C 3.14 • d C 3.14 • 6 C 18.84 The circumference is about 18.8 in. to the nearest tenth. The diameter of a circle is twice as long as the radius r, or d 2r. To find the circumference if you know the radius, replace d with 2r in the formula. C • d • 2r Find the circumference given the diameter.
Find the circumference given the radius.
4. d 9 cm
5. r 13 in.
C•d
C • 2r
C 3.14 • ________
C 3.14 • (2 •
C ___________
C 3.14 • ________
The circumference is ________ cm to the nearest tenth of a centimeter.
C ___________
________)
The circumference is ________ in. to the nearest tenth of an inch.
Find the circumference of each circle to the nearest tenth. Use 3.14 for . 6.
7.
_______________________
8.
________________________
________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
17
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________ LESSON
9-3
Review for Mastery Area of Parallelograms
The area of a figure is the number of square units inside the figure.
You can count the squares inside the rectangle. There are 15 square units within the rectangle. This is equal to 5 • 3.
To find the area of a rectangle, multiply the length ( ) times the width (). A •
Find the area of each rectangle. 1.
2.
Al•w
Al•w
A ______ • ______
A ______ • ______
A ______
A ______
The area is ______ yd2.
The area is ______ in2.
To find the area of a parallelogram, multiply the base b times the height h. Ab•h Find the area of each parallelogram. 4.
3.
Ab•h
Ab•h
A ______ • ______
A ______ • ______
A ______
A ______
The area is ______ yd 2.
The area is ______ cm2.
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
25
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________ LESSON
9-4
Review for Mastery Area of Triangles and Trapezoids
The diagram shows how you can cut a parallelogram into two congruent triangles. Remember that the formula for the area of a parallelogram is A b • h.
1 the area of the parallelogram. 2 1 The formula for the area of a triangle is A • b • h. 2 The area of the triangle is
Find the area of each triangle.
1. A
1 •b•h 2
2. A
1 •b•h 2
A
1 • _____ • _____ 2
A
1 • _____ • _____ 2
A
1 • _____ 2
A
1 • _____ 2
A _____ The area of the triangle is 3.
A _____ _____
2
units .
The area of the triangle is
4.
_______________________
_____
units2.
5.
________________________
________________________
6. What is the area of a triangle with base 16 m and height 10 m? __________________ 7. What is the area of a triangle with base 25 mm and height 50 mm? __________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
33
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________ LESSON
9-4
Review for Mastery Area of Triangles and Trapezoids (continued)
In a trapezoid, the parallel sides are called the bases. One base is always longer than the other. The bases are labeled base 1 and base 2.
Area of trapezoid
1 h(b1 b2) 2
Find the area of each trapezoid.
1 h(b1 b2) 2 1 A • _____ (_____ _____) 2 1 A • _____ (_____) 2 1 A • _____ 2
1 h(b1 b2) 2 1 A • _____ (_____ _____) 2 1 A • _____ (_____) 2 1 A • _____ 2
8. A
9. A
A _____
A _____ The area of the trapezoid is 10.
_____
2
The area of the trapezoid is
in .
11.
_______________________
_____
cm2.
12.
________________________
13. What is the area of a trapezoid with bases 25 yd and 75 yd and height 10 yd?
________________________
_________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
34
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
LESSON
9-5
Review for Mastery Area of Circles
The formula A r2 is used to find the area of a circle. Since the value of is about 3.14, you can use the formula A 3.14 • r • r to estimate the area of a circle. Remember that area is expressed in square units. The radius of the circle is 4 in. A 3.14 • r • r A 3.14 • 4 • 4 A 50.24 The area of the circle is 50.2 in2 to the nearest tenth. Find the area of each circle to the nearest tenth. Use 3.14 for . 1.
2.
The radius is _________ cm.
The diameter is 10 mm.
A r
The radius is _________ mm.
2
A 3.14 • _________ • _________
A r 2
A _____________
A 3.14 • _________ • _________ A _____________
2
The area is _____________ cm to the nearest tenth.
The area is _____________ mm2 to the nearest tenth. 3.
_______________________
4.
5.
________________________
________________________
6. What is the area of a circle with radius 13 yd? Round your answer to the nearest tenth.
______________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
43
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
LESSON
Review for Mastery
9-6
Area of Irregular Figures
When an irregular figure is on graph paper, you can estimate its area by counting whole squares and parts of squares. Follow these steps. • Count the number of whole squares. There are 10 whole squares. • Combine parts of squares to make 1 whole squares or -squares 2 Section 1 1 square • Add the whole and partial squares. 1 1 1 Section 2 1 squares 10 1 1 1 14 2 2 2 1 Section 3 1 squares The area is about 14 square units. 2 Estimate the area of the figure. 1. There are _______ whole squares in the figure. Section 1 _________ square(s) Section 2 _________ square(s) Section 3 _______ square(s) A _________ _________ _________ _________ _________ square units You can break a composite figure into shapes that you know. Then use those shapes to find the area. A (rectangle) 9 · 6 54 m2 A (square) 3 · 3 9 m2 A (composite figure) 54 9 63 m2 Find the area of the figure. 2. A (rectangle) _______ ft2 A (triangle) _______ ft2 A (irregular figure) _______ _______ _______ ft2 Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
44
Holt McDougal Mathematics
8-5
Review for Mastery Classifying Polygons
A polygon is a closed figure that starts and stops at the same point. A polygon is made up of line segments that do not cross. Determine whether each figure is a polygon. If it is not, explain why not. 1.
2.
_______________________
3.
________________________
________________________
Polygons can be classified by the number of sides or angles. The number of sides and angles is the same. Complete the table. Name
Number of Sides
Number of Angles
3
3
4. 5.
Quadrilateral
4
6.
Pentagon
5
7.
Hexagon
8.
Heptagon
6 7
9.
8
10.
Nonagon
11.
Decagon
8
9 10
All the sides of a regular polygon have the same length, and all the angles have the same measure. Determine whether each is a regular polygon. If it is not, explain why not. 12.
13.
_______________________
14.
________________________
________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
44
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________ LESSON
8-6
Review for Mastery Classifying Triangles
All triangles have at least two acute angles. If the third angle is acute, the triangle is an acute triangle.
If the third angle is right, the triangle is a right triangle.
If the third angle is obtuse, the triangle is an obtuse triangle.
A triangle is scalene if each side is a different length.
A triangle is isosceles if two sides are the same length.
A triangle is equilateral if all three sides are the same length.
Use the figure to complete the statements. 1. Each of the 3 angles is less than 90°, so the triangle is an ________________ triangle. 2. The triangle has 3 sides that have the same length, so it is an ________________ triangle. Use the figure to complete the statements. 3. The triangle has a 90° angle, so it is a ________________ triangle.
4. The triangle has 2 sides that have the same length, so it is an ________________ triangle. Use the figure to complete the statements. 5. The triangle has an angle that measures more than 90°, so it is an ________________ triangle. 6. Each side of the triangle has a different length, so it is a ________________ triangle.
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
52
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________ LESSON
8-7
Review for Mastery Classifying Quadrilaterals
Quadrilaterals are polygons that have 4 sides. In the figures below, arrows are used to indicate parallel sides, and tick marks are used to indicate congruent sides. • A trapezoid is a quadrilateral with • A rhombus is a parallelogram with all only one pair of parallel sides. four sides congruent.
• A parallelogram is a quadrilateral with two pairs of parallel sides.
• A square is a rectangle with all four sides congruent.
• A rectangle is a parallelogram with all four angles congruent.
Use the figures to complete the statements. 1. The figure is a __________________ since it has __________________ pair of parallel sides. 2. The figure is a __________________ and a __________________ since it has __________________ pair(s) of parallel sides, and __________________
sides are congruent.
3. The figure is a __________________ and a __________________ and a __________________ and a __________________ since it has __________________
pair(s) of parallel sides,
angles are congruent, and
__________________
__________________
sides are congruent.
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
60
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________ LESSON
8-8
Review for Mastery Angles in Polygons
The sum of the measures of the three angles of any triangle is 180°. To find the missing angle, subtract the sum of the two given angles from 180°. Find the measure of N in triangle LMN. 1. N ______________________ (74° 57°) 2. N ______________________ 131° 3. N ______________________ Find the measure of the unknown angle. 4.
5.
_______________________
6.
________________________
________________________
Use the figures to complete Exercises 7–10. Figure
Number of Sides
7.
Quadrilateral
4
8.
Pentagon
5
9.
Hexagon
6
Number of Triangles
10. The number of triangles is always ___________________ less than the number of sides of the figure. Find the sum of the interior angles. 11.
12.
180° • ______ ______
13.
180° • ______ ______
180° • ______ ______
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
68
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________ LESSON
9-2
Review for Mastery Perimeter and Circumference
The perimeter of any figure is the distance around the figure. Think of perimeter as “going around the rim” of a figure. Find the perimeter of a figure by adding the measures of the sides.
The word perimeter has the word rim in it.
Find the perimeter of each polygon.
P659 P 20
P 7 11 10 8 P 36
The perimeter of the triangle is 20 in.
The perimeter of the quadrilateral is 36 cm.
To find the perimeter of a rectangle, you can add the length and the width and multiply the sum by 2. The formula for the perimeter of a rectangle is P 2( ). P 2( ) P 2(8 5) P 2(13) P 26 The perimeter of the rectangle is 26 feet. Find the perimeter of each polygon. 1.
2.
P _____ _____ _____ P _____ m
3.
P _____ _____ _____ _____
P 2(_____ _____) P _____ cm
P _____ ft
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
16
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________ LESSON
9-2
Review for Mastery Perimeter and Circumference (continued)
The distance around a circle is called the circumference. To find the circumference of a circle, you need to know the diameter or the radius of the circle. C The ratio of the circumference of any circle to its diameter is d always the same. This ratio is known as (pi) and has a value of approximately 3.14. To find the circumference C of a circle if you know the diameter d, multiply times the diameter. C • d, or C 3.14 • d. C•d C 3.14 • d C 3.14 • 6 C 18.84 The circumference is about 18.8 in. to the nearest tenth. The diameter of a circle is twice as long as the radius r, or d 2r. To find the circumference if you know the radius, replace d with 2r in the formula. C • d • 2r Find the circumference given the diameter.
Find the circumference given the radius.
4. d 9 cm
5. r 13 in.
C•d
C • 2r
C 3.14 • ________
C 3.14 • (2 •
C ___________
C 3.14 • ________
The circumference is ________ cm to the nearest tenth of a centimeter.
C ___________
________)
The circumference is ________ in. to the nearest tenth of an inch.
Find the circumference of each circle to the nearest tenth. Use 3.14 for . 6.
7.
_______________________
8.
________________________
________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
17
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________ LESSON
9-3
Review for Mastery Area of Parallelograms
The area of a figure is the number of square units inside the figure.
You can count the squares inside the rectangle. There are 15 square units within the rectangle. This is equal to 5 • 3.
To find the area of a rectangle, multiply the length ( ) times the width (). A •
Find the area of each rectangle. 1.
2.
Al•w
Al•w
A ______ • ______
A ______ • ______
A ______
A ______
The area is ______ yd2.
The area is ______ in2.
To find the area of a parallelogram, multiply the base b times the height h. Ab•h Find the area of each parallelogram. 4.
3.
Ab•h
Ab•h
A ______ • ______
A ______ • ______
A ______
A ______
The area is ______ yd 2.
The area is ______ cm2.
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
25
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________ LESSON
9-4
Review for Mastery Area of Triangles and Trapezoids
The diagram shows how you can cut a parallelogram into two congruent triangles. Remember that the formula for the area of a parallelogram is A b • h.
1 the area of the parallelogram. 2 1 The formula for the area of a triangle is A • b • h. 2 The area of the triangle is
Find the area of each triangle.
1. A
1 •b•h 2
2. A
1 •b•h 2
A
1 • _____ • _____ 2
A
1 • _____ • _____ 2
A
1 • _____ 2
A
1 • _____ 2
A _____ The area of the triangle is 3.
A _____ _____
2
units .
The area of the triangle is
4.
_______________________
_____
units2.
5.
________________________
________________________
6. What is the area of a triangle with base 16 m and height 10 m? __________________ 7. What is the area of a triangle with base 25 mm and height 50 mm? __________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
33
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________ LESSON
9-4
Review for Mastery Area of Triangles and Trapezoids (continued)
In a trapezoid, the parallel sides are called the bases. One base is always longer than the other. The bases are labeled base 1 and base 2.
Area of trapezoid
1 h(b1 b2) 2
Find the area of each trapezoid.
1 h(b1 b2) 2 1 A • _____ (_____ _____) 2 1 A • _____ (_____) 2 1 A • _____ 2
1 h(b1 b2) 2 1 A • _____ (_____ _____) 2 1 A • _____ (_____) 2 1 A • _____ 2
8. A
9. A
A _____
A _____ The area of the trapezoid is 10.
_____
2
The area of the trapezoid is
in .
11.
_______________________
_____
cm2.
12.
________________________
13. What is the area of a trapezoid with bases 25 yd and 75 yd and height 10 yd?
________________________
_________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
34
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
LESSON
9-5
Review for Mastery Area of Circles
The formula A r2 is used to find the area of a circle. Since the value of is about 3.14, you can use the formula A 3.14 • r • r to estimate the area of a circle. Remember that area is expressed in square units. The radius of the circle is 4 in. A 3.14 • r • r A 3.14 • 4 • 4 A 50.24 The area of the circle is 50.2 in2 to the nearest tenth. Find the area of each circle to the nearest tenth. Use 3.14 for . 1.
2.
The radius is _________ cm.
The diameter is 10 mm.
A r
The radius is _________ mm.
2
A 3.14 • _________ • _________
A r 2
A _____________
A 3.14 • _________ • _________ A _____________
2
The area is _____________ cm to the nearest tenth.
The area is _____________ mm2 to the nearest tenth. 3.
_______________________
4.
5.
________________________
________________________
6. What is the area of a circle with radius 13 yd? Round your answer to the nearest tenth.
______________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
43
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
LESSON
Review for Mastery
9-6
Area of Irregular Figures
When an irregular figure is on graph paper, you can estimate its area by counting whole squares and parts of squares. Follow these steps. • Count the number of whole squares. There are 10 whole squares. • Combine parts of squares to make 1 whole squares or -squares 2 Section 1 1 square • Add the whole and partial squares. 1 1 1 Section 2 1 squares 10 1 1 1 14 2 2 2 1 Section 3 1 squares The area is about 14 square units. 2 Estimate the area of the figure. 1. There are _______ whole squares in the figure. Section 1 _________ square(s) Section 2 _________ square(s) Section 3 _______ square(s) A _________ _________ _________ _________ _________ square units You can break a composite figure into shapes that you know. Then use those shapes to find the area. A (rectangle) 9 · 6 54 m2 A (square) 3 · 3 9 m2 A (composite figure) 54 9 63 m2 Find the area of the figure. 2. A (rectangle) _______ ft2 A (triangle) _______ ft2 A (irregular figure) _______ _______ _______ ft2 Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
44
Holt McDougal Mathematics
