Download Similar Triangles or Not? - IHS Math

LESSON 6.2
Assignment
Name
me
Date
te
Similar Triangles or Not?
Similar Triangle Theorems
‹___›
‹___›
1. In the figure below, NS || BE . Use the information given in the figure to determine the m/SNA,
m/NAS, m/ABE, and m/BAE. Is nNSA similar to nEBA? If the triangles are similar, write a
similarity statement. Use complete sentences to explain your answers.
B
N
A
328
858
E
S
The measure of angle SNA is 328, because alternate interior angles between parallel lines
have the same measure.
© Carnegie Learning
The measure of angle ABE is 858, because alternate interior angles between parallel lines
have the same measure.
The measure of angle NAS and the measure of angle BAE is 638, because vertical angles
are congruent. The sum of the measures of the interior angles in a triangle is 1808.
So, m/NAS 5 m/BAE 5 1808 2 858 2 328 5 638. Therefore, nNSA , nEBA because
of Angle-Angle Similarity Postulate.
6
Chapter 6 Assignments
119
LESSON 6.2
Assignment
page 2
2. Use a ruler to determine whether the triangles shown are similar. Explain your answer.
E
DE = 1.5 cm
D
EF = 6 cm
F
DF = 7 cm
AC = 14 cm
C
A
AB = 3 cm
BC = 12 cm
B
___ ___ ___
All of the corresponding sides are proportional: 3 5 12 5 14 5 2.
1.5
7
6
© Carnegie Learning
So, the triangles are similar by the Side-Side-Side Similarity Postulate.
6
120
Chapter 6
Assignments
LESSON 6.2
Assignment
page 3
Name
me
Date
te
___
___
3. In the figure shown, NU || CV . Use the figure to complete part (a) through part (c).
M
U
N
V
C
a. Is /MUN > /MCV ? Explain your answer.
Yes. Segments NU and CV are parallel and angles MUN and MCV are corresponding angles.
When two parallel lines are intersected by a transversal, then the corresponding angles are
congruent. So, angles MUN and MCV are congruent.
b. Is /MNU > /MVC ? Explain your answer.
© Carnegie Learning
Yes. Segments NU and CV are parallel and angles MNU and MVC are corresponding angles.
When two parallel lines are intersected by a transversal, then the corresponding angles are
congruent. So, angles MNU and MVC are congruent.
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c. Is nCMV , nUMN ? Explain your answer.
Yes. Angles MUN and MCV are congruent and angles MNU and MVC are congruent, so by the
Angle-Angle Similarity Postulate nCMV , nUMN.
Chapter 6 Assignments
121
LESSON 6.2
Assignment
page 4
4. In the figure shown, segments AB and DE are parallel. The length of segment BC is 10 units and the
length of segment CD is 5 units. Use this information to calculate the value of x. Explain how you
determined your answer.
2x + 5
D
E
5
C
10
A
B
11x – 4
Segments AB and DE are parallel, so by the Corresponding Angles Postulate angles A and E are
congruent and angles B and D are congruent. In addition, by the Vertical Angles Congruence
Postulate angles DCE and BCA are congruent because they are vertical angles. So, by the AngleAngle Similarity Postulate triangles ACB and ECD are similar and the ratios of the corresponding
side lengths are equal.
10
11x 2 4 5 ___
________
5
2x 1 5
5(11x 2 4) 5 10(2 x 1 5)
55x 2 20 5 20x 1 50
35x 5 70
x52
© Carnegie Learning
So, the value of x is 2 units.
6
122
Chapter 6
Assignments