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000200010271713722_CH06_L01.qxp
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2/5/13
6:31 PM
Page 2
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Date
Reteaching 6-1
Angle Measures
Acute angles have a measurement of less than 90. In the diagram
below, &1 and &2 are acute angles.
Obtuse angles have a measurement of more than 90. In the diagram,
&5 is an obtuse angle.
Vertical angles are formed across from each other where two lines
intersect. They always have equal measurements. In the diagram,
&1 and &4 are vertical angles. They both measure 50.
3
2
50 1
4
5
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When the sum of two angles is 90, the angles are complementary.
In the diagram, &1 and &2 are complementary angles. To find the
measurement of a complementary angle, subtract from 90.
90 - m&1 = m&2
90 - 50 = m&2
40 = m&2
m&2 = 40
When the sum of two angles is 180, the angles are supplementary.
In the diagram, &4 and &5 are supplementary angles. To find the
measurement of a supplementary angle, subtract from 180.
180 - 50 = m&5
130 = m&5
m&5 = 130
Use the diagram to find the measurement of each angle.
Then classify each angle as obtuse, right, or acute.
146
A
1. &A
2. &B
B
C
D
40
3. &C
4. &D
5. Angles 1 and 2 are supplementary. If angle 1 measures (2x 2)°,
and angle 2 measures (x 5)°, what is the measure of each angle?
Course 2 Lesson 6-1
Reteaching
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180 - m&4 = m&5
2/5/13
5:10 PM
Page 2
Name
Class
Date
Reteaching 6-2
Area of a Parallelogram
You can use the area of a rectangle to find the area of
a parallelogram.
1
2
3
4 cm
Draw a perpendicular segment from one vertex to the
opposite side to form a triangle.
8 cm
Move the triangle to the right side of the parallelogram
to form a rectangle.
4 cm
Find the area of the rectangle.
A = length width = base height = bh
8 cm
A = bh
A=8?4
A = 32 cm2
The parallelogram has the same base, height, and area
as the rectangle.
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000200010271713722_CH06_L02.qxd
Find the area of each figure.
1.
2.
6 cm
3.
5m
5 cm
8 ft
7m
4.
5.
4.3 in.
6.
0.7 ft
3.6 in.
2.1 in.
0.9 ft
7.2 in.
Find the area of a parallelogram with base length b and height h.
7. b 7 in., h 4 in.
Course 2 Lesson 6-2
8. b 9 m, h 1.5 m
9. b 1.25 cm, h 2 cm
Reteaching
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4 ft
000200010271713722_CH06_L03.qxd
2/6/13
11:15 AM
Name
Page 2
Class
Date
Reteaching 6-3
Area of a Triangle
You can use the area of a parallelogram to find the area of
a triangle. Two identical triangles, together as shown, form
a parallelogram. Each triangle has half the area of
the parallelogram.
4 cm
Area of parallelogram: A bh
Area of triangle:
A
1
2 bh
1
2
7 cm
? 7 ? 4 14
cm2
This triangle has an area of 14 cm2.
1.
2.
3.2 ft
10 cm
6 cm
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Find the area of each triangle.
3.
3.2 m
3.2 ft
5m
4.
7.8 cm
Solve.
5. Ryan took measurements of his new kite and made the drawing
shown on the right.
in.
6
.
7
4.1 in.
What is the area of Ryan’s kite?
in.
12.4
17.4 in.
10.3 in.
Course 2 Lesson 6-3
Reteaching
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
9 cm
000200010271713722_CH06_L04.qxd
3/20/13
9:09 PM
Page 2
Name
Class
Date
Reteaching 6-4
Areas of Other Figures
Trapezoid
Irregular Figures
Two identical trapezoids, together as shown, form
a parallelogram. The trapezoid has half the area
of the parallelogram.
Not all geometric figures are shapes with which
you are familiar. Some of them, however, can be
7 ft
divided into familiar shapes.
Find the area of the figure.
6 ft
10 ft
Use the area formulas to find
the areas of the triangle and
the rectangle.
5 12 (2)(4)
A 5 12 h(b1 1 b2)
Area of trapezoid:
5 12bh
5 12 (8)
5 12 (4)(10 1 8)
4 ft
2 ft
7 ft
5 4 ft2
⫽ 2(18) ⫽ 36 in.2
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Area of a triangle
Area of parallelogram: A 5 (b1 1 b2)h
9 ft
Area of a rectangle ⫽ bh
⫽ (7)(10)
⫽ 70 ft2
10 ft
Total area ⫽ area of triangle ⫹ area of rectangle
⫽ 4 ⫹ 70
⫽ 74
The total area is 74 ft2.
Based on appearance, find the area of each figure.
1.
2.
48 ft
22 ft
4 ft
7 ft
3.
3 12 in.
9 12 in.
20 ft
6 ft
4.
5.
7m
6.
26 km
4m
17 km
11 m
Course 2 Lesson 6-4
36 yd
37 yd
11 km
46 km
13 m
20 yd
80 yd
Reteaching
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Find the total area by adding
the area of each figure.
000200010271713722_CH06_L05.qxd
2/5/13
5:09 PM
Page 2
Name
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Reteaching 6-5
Date
Circumference and Area of a Circle
The circumference of a circle is the distance around it. To find the
circumference of a circle with radius r and diameter d, use either
the formula C = 2pr or C = pd. Use 3.14 for p.
d ⫽ 8 cm
C ⫽ pd
≈ 3.14 ? 8
⫽ 25.12 cm
6 ft
To the nearest centimeter, the
circumference is 25 cm.
To the nearest foot, the
circumference is 38 ft.
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8 cm
r ⫽ 6 ft
C ⫽ 2pr
≈ 2 ? 3.14 ? 6
⫽ 37.68 ft
To find the area of a circle, use A ⫽ pr2.
The diameter of the circle is 8 cm, so the radius is 4 cm.
8 cm
A = pr2
≈ 3.14 ? 4 ? 4
⫽ 50.24 cm2
To the nearest square centimeter, the area is 50 cm2.
2.
3.
in
.
1.
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Find the circumference and area of each circle. Round your
answer to the nearest whole unit.
4.
10
2
7 cm
5.
m
6.
2 cm
8y
d
3 ft
Course 2 Lesson 6-5
Reteaching