Pairs of Angles

1
Pairs of Angles
LESSON 7-1
Problem of the Day
Students at West Ridge Middle School are going on
a trip to the museum. Nine have never gone
before. Twelve have gone once, half as many as
that have gone twice, and none have gone more
than that. How many students are going on the
trip?
27
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Pairs of Angles
LESSON 7-1
Check Skills Youll Need
(For help, go to Lesson 1-6.)
1. Vocabulary Review What is the inverse
operation of addition?
Solve each equation.
2. a 14 32
3. b 5 26
4. 10 c 31
5. 48 d 19
Check Skills Youll Need
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Pairs of Angles
LESSON 7-1
Check Skills Youll Need
Solutions 1. subtraction 2. 18 3. 31 4. 4
1 5. 29
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Pairs of Angles
LESSON 7-1
Additional Examples
Find the measure of the supplement of ? IGJ.
Quick Check
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Pairs of Angles
LESSON 7-1
Additional Examples
Name a pair of adjacent angles and a pair of
vertical angles in the figure. Find m HGK.
Quick Check
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Pairs of Angles
LESSON 7-1
Additional Examples
In this figure, if m DKH 73, find the
measures of GKJ and JKF.
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Pairs of Angles
LESSON 7-1
Additional Examples
(continued)
Quick Check
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Pairs of Angles
LESSON 7-1
Lesson Quiz
Use the diagram to answer Questions 1
3. 1. List all pairs of vertical
angles. 2. List any angles adjacent to
CXD. 3. If m AXB 110, find m
DXC. 4. An angle measures 57. What is the
measure of its supplement?
110
123
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Angles and Parallel Lines
LESSON 7-2
Problem of the Day
Write the following sentence in mathematical
symbols. Then indicate whether the sentence is
true or false Four and one sixth minus five
eighths equals three and thirteen twenty fourths.
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Angles and Parallel Lines
LESSON 7-2
Check Skills Youll Need
(For help, go to Lesson 7-1.)
1. Vocabulary Review Which of the following
pairs of angles are supplementary?
50 and 40, 100 and 90, 120 and 60, 75 and
125
Find the measure of the supplement of each angle.
2. 48
3. 119
4. 67
5. 131
Check Skills Youll Need
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Angles and Parallel Lines
LESSON 7-2
Check Skills Youll Need
Solutions 1. 120 and 60 2. 132 3. 61 4
. 113 5. 49
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Angles and Parallel Lines
LESSON 7-2
Additional Examples
Identify each pair of corresponding angles and
each pair of alternate interior angles.
Quick Check
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Angles and Parallel Lines
LESSON 7-2
Additional Examples
If p is parallel to q, and m 3 56º, find m
6.
Quick Check
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Angles and Parallel Lines
LESSON 7-2
Additional Examples
In the diagram below, m 5 m 6 and m 7
80º. Explain why p and q are parallel and why s
and t are parallel.
Quick Check
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Angles and Parallel Lines
LESSON 7-2
Lesson Quiz
Use the diagram to answer the questions. 1.
Classify 4 and 7 as 2. Classify 2 and
8 as alternate interior angles, alternate
interior angles, corresponding angles,
corresponding angles, or neither. or
neither. 3. If a b and m 8 80,
4. Suppose m 5 100 and find m 4. m
3 100. What can you conclude about line a
and line b?
neither
alternate interior angles
80
a b
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Congruent Polygons
LESSON 7-3
Problem of the Day
Solve the proportion .
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Congruent Polygons
LESSON 7-3
Check Skills Youll Need
(For help, go to Lesson 4-4.)
1. Vocabulary Review Congruent angles have ?
measures.
Are the polygons similar?
Explain. 2.
Check Skills Youll Need
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Congruent Polygons
LESSON 7-3
Check Skills Youll Need
Solutions 1. equal 2.
not similar corresponding sides are
not in proportion.
LN ZY
LM XZ
5 15
4 10
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Congruent Polygons
LESSON 7-3
Additional Examples
In the diagram below, list the congruent parts
of the two figures. Then write a congruence
statement.
Quick Check
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Congruent Polygons
LESSON 7-3
Additional Examples
Show that each pair of triangles is congruent.
b.
a.
Quick Check
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Congruent Polygons
LESSON 7-3
Additional Examples
A surveyor drew the diagram below to find the
distance from J to I across the canyon. Show that
GHI KJI. Then find JK.
Corresponding parts of congruent triangles are
congruent. JK corresponds to HG, so JK is 36 ft.
Quick Check
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Congruent Polygons
LESSON 7-3
Lesson Quiz
Use ABC and XYZ to answer the
questions. 1.Suppose AC XZ, AB XY,
and BC YZ. Write a congruence
statement for the figures. 2. Suppose
ABC and XYZ are congruent. If AB 5 cm,
BC 8 cm, and AC 10 cm, find
XZ. 3. Suppose B Y, A
X, and AB XY. Why is ABC
XYZ?
?ABC ? ?XYZ
10 cm
ASA
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Congruent Polygons
LESSON 7-3
Lesson Quiz
4. Let AB XY 9 inches BC YZ 24 inches
and m B 85, m Z 35, and m Y 85.
Prove that the triangles are congruent and
find m C.
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Classifying Triangles and Quadrilaterals
LESSON 7-4
Problem of the Day
Ruth was born on February 29, 1984. If she
insists on celebrating her birthday only on
February 29, when will she celebrate her 12th
birthday?
2032
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Classifying Triangles and Quadrilaterals
LESSON 7-4
Check Skills Youll Need
(For help, go to the Skills Handbook page 640.)
1. Vocabulary Review How many degrees does a
right angle have?
Classify each angle as acute, right,
obtuse, or straight. 2. 3.
Check Skills Youll Need
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Classifying Triangles and Quadrilaterals
LESSON 7-4
Check Skills Youll Need
Solutions 1. 90 2. acute 3. obtuse
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Classifying Triangles and Quadrilaterals
LESSON 7-4
Additional Examples
Classify LMN by its sides and angles.
The triangle has two sides that are congruent and
three acute angles. It is an isosceles acute
triangle.
Quick Check
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Classifying Triangles and Quadrilaterals
LESSON 7-4
Additional Examples
What is the best name for figure WXYZ?
Explain your choice.
WXYZ has both pairs of opposite sides parallel,
but adjacent sides are not equal, so it is a
parallelogram.
Quick Check
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Classifying Triangles and Quadrilaterals
LESSON 7-4
Lesson Quiz
1. Classify the triangle according to its angles
and sides. 3. Determine the best name
for the quadrilateral.
obtuse isosceles triangles
2. A triangles sides are all congruent and its
angles all measure 60. Classify the triangle.
equilateral, acute
rhombus
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Classifying Triangles and Quadrilaterals
LESSON 7-4
Lesson Quiz
4. What is the best name for a figure that has
four sides
congruent, corresponding sides parallel, and all
four angles congruent?
square
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Angles and Polygons
LESSON 7-5
Problem of the Day
A pound of turkey has 144 g of protein and will
serve 4 people. If 4 people are served equal
amounts, how many grams of protein will each
receive?
36 g
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Angles and Polygons
LESSON 7-5
Check Skills Youll Need
(For help, go to the Lesson 1-1.)
1. Vocabulary Review How do you evaluate an
algebraic expression?
Evaluate each expression for a 8. 2.
3(a 1) 3.
5a 8
a
4. (a 2)6
Check Skills Youll Need
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Angles and Polygons
LESSON 7-5
Check Skills Youll Need
Solutions 1. You replace each variable in
the expression with a number and then
simplify. 2. 27 3. 6 4. 36
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Angles and Polygons
LESSON 7-5
Additional Examples
Find the sum of the measures of the interior
angles of an octagon.
An octagon has 8 sides.
The sum of the interior angles of an octagon is
1,080.
Quick Check
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Angles and Polygons
LESSON 7-5
Additional Examples
Find the missing angle measure in the hexagon.
Step 1 Find the sum of the measures of the
interior angles of a hexagon.
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Angles and Polygons
LESSON 7-5
Additional Examples
(continued)
Step 2 Write an equation.
Let x the missing angle measure.
The missing angle measure is 122º.
Quick Check
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Angles and Polygons
LESSON 7-5
Additional Examples
A design on a tile is in the shape of a regular
nonagon. Find the measure of each angle.
Each angle of a regular nonagon has a measure of
140.
Quick Check
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Angles and Polygons
LESSON 7-5
Lesson Quiz
1. Find the sum of the measures of the interior
angles of a polygon having 17
sides. 2. Five angles of a hexagon measure
128, 190, 112, 154, and 90. Find the
measure of the missing angle. 3. Find the
measure of each angle of a regular polygon having
24 sides.
2,700
46
165
4. A regular figure has an interior angle measure
of 135. How many sides does it have?
8
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Areas of Polygons
LESSON 7-6
Problem of the Day
Lucy predicted that her final average for math
class would be at least a 93. Her test grades
were 88, 90, 92, 97. What is the lowest test
score she can make on the last test to make this
true?
98
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Areas of Polygons
LESSON 7-6
Check Skills Youll Need
(For help, go to Lesson 2-6.)
1. Vocabulary Review What is a formula?
Find the area of each figure. 2. 3.
Check Skills Youll Need
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Areas of Polygons
LESSON 7-6
Check Skills Youll Need
Solutions 1. A formula is a rule that shows the
relationship between two or more
quantities. 2. A w 3. A s2 10
8 72 A 80 cm2 A 49
ft2
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Areas of Polygons
LESSON 7-6
Additional Examples
Find the area of the triangular part of the
doghouse.
The area of the triangular part of the doghouse
is 378 in.2.
Quick Check
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Areas of Polygons
LESSON 7-6
Additional Examples
Find the area of the trapezoid.
The area of the trapezoid is 35.2 in.2.
Quick Check
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Areas of Polygons
LESSON 7-6
Lesson Quiz
1. Find the area.
14 cm2
2. An architect is designing a restaurant with a
triangular entrance. The base of the triangle
is 10 ft wide. The entrance is 14 ft tall.
Find the area of the triangle.
70 ft2
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Areas of Polygons
LESSON 7-6
Lesson Quiz
3. Find the area.
56 ft2
4. If both bases of the figure in Exercise 3 are
doubled, what is the new area of the
trapezoid?
112 ft2
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Circumference and Area of a Circle
LESSON 7-7
Problem of the Day
Opal, Charles, Jean, and Scott had an
earthworm-catching contest. Jean caught one
fourth as many worms as Opal and twice as many as
Charles. Opal caught 3 times as many worms as
Scott. How many worms did each of the other three
contestants catch if Scott caught 8 worms?
Opal, 24 Jean, 6 Charles, 3
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Circumference and Area of a Circle
LESSON 7-7
Check Skills Youll Need
(For help, go to Lesson 7-6.)
1. Vocabulary Review Explain the difference
between perimeter and area.
Find the area of the figure below. 2.
Check Skills Youll Need
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Circumference and Area of a Circle
LESSON 7-7
Check Skills Youll Need

• Solutions
• 1. Perimeter is the distance around a figure.
  Area is the number of square
• units a figure encloses.
• 2. A bh
• 13 7

A 45.5 ft²
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Circumferences and Areas of Circles
LESSON 7-7
Additional Examples
The diameter of a tractor tire is 125 cm. Find
the circumference and area. Round to the nearest
tenth.
The circumference is about 392.7 cm.
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Circumferences and Areas of Circles
LESSON 7-7
Additional Examples

(continued)
Use the formula for the area of a circle.
The area is about 12,271.8 cm2.
Quick Check
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Circumferences and Areas of Circles
LESSON 7-7
Additional Examples
Find the area of the unshaded region of the
square tile with a circle inside of it, as shown
below. Round to the nearest tenth.
You can separate the figure into a circle and a
square.
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Circumferences and Areas of Circles
LESSON 7-7
Additional Examples
(continued)
Step 1 Find the area of the square.
Area of square s2
Step 2 Find the area of the circle.
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Circumferences and Areas of Circles
LESSON 7-7
Additional Examples
(continued)
Step 3 Subtract the area of the circle from the
area of the square.
The area of the shaded region is about 144 cm2
113.1 cm2 30.9 cm2.
Quick Check
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Circumferences and Areas of Circles
LESSON 7-7
Lesson Quiz
1. Find the circumference and area of the
circle. Round to the nearest
tenth. 2. The diameter of the lid
of a can of soup is 5 cm. Find its
circumference and area. Round to the nearest
tenth.
18.8 km 28.3 km2
15.7 cm 19.6 cm2
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Circumferences and Areas of Circles
LESSON 7-7
Lesson Quiz
3. Find the area. Round to the nearest tenth.
273.0 in.2
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Constructions
LESSON 7-8
Problem of the Day
Estimate in years the age of someone who is a
million minutes old.
about 2 yr
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Constructions
LESSON 7-8
Check Skills Youll Need
(For help, go to Lesson 7-3.)
1. Vocabulary Review How are congruent
polygons the same?
List the congruent parts of each pair of
congruent figures. 2. ?PQR ?TUV
3. ABCD LMNO
Check Skills Youll Need
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Constructions
LESSON 7-8
Check Skills Youll Need
Solutions 1. Congruent polygons have the same
size and shape. 2. P T Q U
R V PQ TU QR UV RP
VT
3. A L B M C N
AB LM BC MN CD NO
D O

DA OL
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Constructions
LESSON 7-8
Additional Examples
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Constructions
LESSON 7-8
Additional Examples
(continued)
Quick Check
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Constructions
LESSON 7-8
Additional Examples
Draw a line f. Construct a line parallel to line
f.
Quick Check
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Constructions
LESSON 7-8
Lesson Quiz
For Exercises 12, use the diagram below.
1. Construct an angle that is congruent to ?R.
2. Construct a line parallel to RS.
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