Name
Date
Class
California Standards MG2.3
LESSON
Review for Mastery
9-8 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 rhombus is a parallelogram with all
four sides congruent.
• A trapezoid is a quadrilateral with only
one pair of parallel sides.
• 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
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sides are congruent.
73
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California Standards MG2.3
California Standards Extension of
Review for Mastery
LESSON
LESSON
9-9 Congruent Figures
9-8 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.
When two polygons are congruent, the angles and the sides of one
polygon are equivalent to the corresponding angles and sides of the
other polygon.
• A rhombus is a parallelogram with all
four sides congruent.
• A trapezoid is a quadrilateral with only
one pair of parallel sides.
Find the corresponding side or angle.
1. 苶
AB
苶
2. ⬔DAB 3. 苶
GH
苶
• A parallelogram is a quadrilateral with
two pairs of parallel sides.
MG2.2
Review for Mastery
• A square is a rectangle with all four
sides congruent.
4. ⬔GFE ABCD EFGH
苶F
E
苶
⬔HEF
6 cm
D
苶D
C
苶
⬔CBA
F 9 cm E
A 9 cm B
6 cm
8 cm
8 cm
H
14 cm C
14 cm
G
To show that two triangles are congruent, you can show that the
three sides of one triangle are congruent to the three sides of the
other triangle. This is called the Side-Side-Side rule.
• A rectangle is a parallelogram with all
four angles congruent.
P
苶Q
苶苶
ST
苶 since both are 8 inches.
6 in.
P
Q
苶R
苶苶
TU
苶 since both are 6 inches.
U
8 in.
PR
苶
苶苶
SU
苶 since both are 10 inches.
T
10 in.
8 in.
10 in.
So, 䉭PQR 䉭STU.
S
Q 6 in. R
If you know that two figures are congruent, you can find missing
measures in the figures.
Use the figures to complete the statements.
trapezoid
1. The figure is a
• The corresponding angles are in the
same position.
one
since it has
• The corresponding sides are in the
same position.
pair of parallel sides.
parallelogram
2. The figure is a
two
since it has
four
Complete.
pair(s) of parallel sides, and
rectangle
two
and a
square
four
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AF1.1, AF1.2, AF3.1, AF3.2
74
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California Standards
Review for Mastery
LESSON
10-1 Perimeter
AF1.1, AF3.1, AF3.2,
Holt Mathematics
MG1.1, MG1.2
Review for Mastery
LESSON
10-2 Circles and Circumference
The perimeter of a figure is the distance around it. To find the
perimeter of a figure, find the sum of the lengths of its sides.
A circle is the set of all points in a plane that are the same distance
from a given point, called the center.
Look at the figure below.
4.2
A line segment with an endpoint at the center and an endpoint at
the circle is called the radius r. A line segment that passes through
the center and has both endpoints on the circle is called the
diameter d. The length of the diameter is twice the radius.
2.3
The perimeter is the sum of the lengths of
its sides.
P 2.3 1.5 3.4 4.2
11.4
So, the perimeter of the figure is 11.4 units.
3.4
1.5
W
? ?
7 in.
7. What is the length of
9 in.
VW
苶
苶?
苶
苶苶
XY
苶, so the length of 苶
LM
苶
LM
7 in.
is
73
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California Standards
6. JKLMN VWXYZ
sides are congruent.
100° 7 in.
V
J 115°
L X
110°
110° 115°
6 in.
6 in.
7 in.
?
100° 115°
115° 100°
N 8 in. M
Y 8 in. Z
since it has
four
pair(s) of parallel sides,
angles are congruent, and
9 in.
⬔K ⬔W, so the measure of ⬔W
100°
is
.
rhombus
and a
K
5. JKLMN VWXYZ
sides are congruent.
parallelogram
3. The figure is a
and a
rhombus
and a
This is circle P.
QR
苶
苶 is a diameter.
P
苶Q
苶 and P
苶R
苶 are radii.
Q
R
P
Find the perimeter of each figure.
1.
2
2.
2
2
4
3
2
2
1 3 1
1
Identify each part of the circle below.
1 3
3
4
1. circle
1
2
4
7
3
2
3
26 units
30 units
苶B
A
苶 and A
苶C
苶
d6
23 18 20 11 72
94 72 22
C
To find the circumference C of a circle, use a formula.
Then subtract the sum from the perimeter.
20
A
22
To find the missing length x first find the sum
of the known lengths.
23
3. two radii
B
Pi is a decimal number that has no end and never repeats. 3.14 or 7
is used to estimate pi.
The perimeter of the figure below is 94 units.
18
苶C
B
苶
The distance around a circle is called the circumference. The ratio of
the circumference of a circle to its diameter is always the same. This
relationship is called pi and is represented by the Greek letter ␲.
If you know the perimeter of a figure, you can find the unknown
length of a side.
11 x
A
2. diameter
C ␲d
⬇ 3.14 6
⬇ 18.84
The circumference is about 18.84 units.
So, side x is 22 units long.
Find the circumference. Use 3.14 as an estimate for ␲.
Find the missing length for each figure.
3.
5
4.
4.
13
13
2
2
2
Perimeter 34 units
x 12 units
x 6 units
75
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5
x
Perimeter 30 units
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All rights reserved.
d4
2
2
x
5.
d8
C 25.12 units
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19
C 12.56 units
76
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Holt Mathematics