Chapter_19_files/Chapter 19 Reteach

Name
Chapter 19, Lesson 1
Reteach
Date
Hands On: Sums of Angle Measures
CA Standards
MG 2.2,
MG 2.1
Find the sum of the measures of angles in triangles and in
quadrilaterals.
Find the sum of the measures of the
angles in a triangle.
Find the sum of the measures of the
angles in a rectangle.
Step 1 Use a straightedge to draw a
triangle. Cut out the triangle. Label the
angles a, b, and c.
Step 1 Use a straightedge to draw a
quadrilateral. Label the angles a, b, c, and d.
Step 2 Draw a line segment connecting
one vertex to the opposite vertex. Cut the
quadrilateral along the line you drew.
a
b
a
b
d
c
c
Step 2 Tear off the three angles of the
triangle.
Step 3 Use a straightedge to draw a
straight angle.
Step 4 Arrange the angles of the triangle
so they meet at a point and lie on the
straight angle.
What is the sum of the measures of the
angles in a triangle?
°
180
Step 3 What is the sum of the angles in
each of the pieces?
Place the pieces together to make your
original quadrilateral.
What is the sum of the measures of the
angles in a quadrilateral?
°
360
Trace each figure. Use scissors and a straight angle to find the sum of
the measures of the angles for each figure.
1.
2.
3.
4.
60
Writing Math How are the measures of the angles of a triangle
different from the measures of the angles of a quadrilateral?
Reteach
Copyright © Houghton Mifflin Company. All rights reserved.
19–6
Use with text pages 410–411.
Name
Chapter 19, Lesson 1
Homework
Date
Hands On: Sums of Angle Measures
CA Standards
MG 2.1
MG 2.2,
Find the sum of the measures of the angles in a triangle.
Step 1
Use a straightedge to draw any triangle.
Cut it out. Label the angles a, b, and c.
Make triangle different from the one in Reteach.
Place triangle to the right of the Steps.
Step 2
Tear off the three angles of the triangle.
Step 3
Use a straightedge to draw a straight angle.
Arrange the angles of the triangle so they
meet at a point and lie on the straight angle.
a
c
b
The sum of the measures of the angles in a triangle is 180°.
Find the sum of the measures of the angles in a quadrilateral.
1.
Use a straightedge to draw any quadrilateral. Label the angles a, b, c, and d.
a
b
d
2.
On your quadrilateral, draw a line segment connecting one vertex to the opposite vertex.
Cut the quadrilateral along the line you drew. Place the pieces together to fit into your
original quadrilateral.
a
b
d
3.
c
c
What is the sum of the measures of the angles in a quadrilateral?
4QJSBM3FWJFX
(Chapter 15, Lesson 5) KEY NS 2.2
Solve.
4.
1,305 ÷ 15
6.
Barbara’s Bakery baked 25,248 cookies. One cookie bag holds 24 cookies. How many
bags will the bakery need to use to hold all of the cookies?
Homework
Copyright © Houghton Mifflin Company. All rights reserved.
5.
19–10
12,450 ÷ 30
Use with text pages 410–411.
Name
Chapter 19, Lesson 2
Reteach
Date
Triangles
CA Standards
MG 2.2, MG 2.0
You can classify triangles by the length of their sides.
Equilateral Triangle
Isosceles Triangle
Scalene Triangle
2 in.
2 ft
2 ft
10 in.
2 ft
10 in.
5 in.
6 in.
4 in.
All sides are the same
length.
At least two sides are the same No sides are the same length.
length.
You can classify triangles by their angles.
Right Triangle
65˚
90˚
Obtuse Triangle
35˚
25˚
One right angle
Acute Triangle
15˚
130˚
75˚
45˚
One obtuse angle
60˚
All acute angles
Classify each triangle in two ways.
1.
2.
40˚
x
15˚
3.
x
10 cm
45˚
x
25 cm
136˚
22˚
10 cm
Writing Math Can a triangle have two right angles? Explain.
Reteach
Copyright © Houghton Mifflin Company. All rights reserved.
19–12
Use with text pages 412–414.
Name
Chapter 19, Lesson 3
Reteach
Date
Quadrilaterals
CA Standards
MG 2.2, MG 2.0
Classify quadrilaterals and find missing angle measures.
A quardrilateral is a four-sided figure. The sum of the angle measures in any quadrilateral is
360°. A quadrilateral can be classfied by its sides and angles.
Quadrilaterals
Rectangle
Square
2 ft
Four right
angles
four sides
Opposite
sides are the
same length
four angles
Trapezoid
4 ft
4 ft
2 ft
Parallelogram
One pair of
parallel sides
Four sides
are the same
length
3 in.
3 in.
3 in.
Four right
angles
3 in.
Rhombus
Opposite sides
are parallel
and the
same length
7c
m
°
35
°
m
4c
5
14
1
m
4c
1
°
45
1
°
35
7c
m
Four sides
are the same
length
5 ft
110
70
5 ft
5 ft
Opposite sides
are parallel
70
110
5 ft
Classify each figure in as many ways as possible. Then find the missing angle measure.
1.
5 cm
5 cm
2.
x
5 cm
12 ft
85
95
6 ft
x
85
5 cm
3.
x
4 in.
6 ft
12 ft
4 in.
70
70
110
4 in.
4 in.
Writing Math Can a trapezoid also be classified as a
parallelogram? Explain why or why not.
Reteach
Copyright © Houghton Mifflin Company. All rights reserved.
19–18
Use with text pages 416–418.
Name
Chapter 19, Lesson 4
Reteach
Date
Congruence
CA Standards
MG 2.1, MG 2.0
Identify congruent figures using two methods.
Janie is making a scrapbook using pictures of
her camping trip. She wants the figures in her
album to be the same size and same shape.
Are triangles GHJ and LMN congruent?
M
H
J
G
N
L
Use a Tracing
Use a Ruler and Protractor
Step 1
Step 1 Use a ruler to measure the sides of
triangle GHJ and triangle LMN.
Trace triangle GHJ.
Step 2 Place your tracing on top of
triangle LMN.
The figures are the same size and shape, so
they are congruent: !GHJ " !LMN
Step 2 Use a protractor to measure the
angles of triangle GHJ and triangle LMN.
The sides and angles of both triangles
have the same measure, so the figures are
congruent: !GHJ " !LMN .
Determine if the two figures are congruent. Write yes or no.
1.
Figure 2
2. Figure 1
Figure 2
Figure 1
3.
4.
Writing Math Use one of the methods on this page to
determine whether the figures at the right are congruent.
Explain why you chose your method.
Reteach
Copyright © Houghton Mifflin Company. All rights reserved.
19–24
A
B
Use with text pages 420–421.
Name
Date
Problem Solving: Missing Angle
Problems
Chapter 19, Lesson 5
Reteach
CA Standards
MR 2.3,
MG 2.2
Kara is making a shelf for a corner of her room. The shelf is the shape of a right triangle. One
of the angle measures is 50°. What are the measures of the other two angles?
Understand
Plan
One of the angles is 50°.
Add the measures of the two angles you know.
The triangle formed is a right triangle, so one
angle is 90°.
Subtract the sum from 180° to find the
measure of the third angle.
The sum of the measures of the angles in any
triangle is 180°.
Solve
Look Back
50°
180°
+ 90°
- 140°
140°
40°
Did you answer the question that was asked?
Add the measures of the three angles. Do they
total 180°?
The measures of the angles of the triangle are
40°, 50°, and 90°.
Use the angles you know to solve each problem. Show your work.
1.
Reuben is making repairs to his house. He has leaned a piece of plywood against the wall
of his dining room. The plywood, floor, and wall form a right triangle. The plywood and the
wall form a 20° angle. What are the measures of the other two angles of the triangle?
2.
Kelly’s backyard is in the shape of a quadrilateral. She is building a new fence, so she
has measured the angles at the corners of the yard. The first three angle measures are
110°, 80°, and 70°. What is the angle measure of the fourth corner?
Writing Math Explain how to find the missing angle for a triangle.
Reteach
Copyright © Houghton Mifflin Company. All rights reserved.
19–30
Use with text pages 422–423.

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