6-2
Properties of
Parallelograms
PART 2
Vocabulary
Review
1. Multiple Choice What does bisect mean?
to cross at a point
to divide into two equal parts
to reflect across a line
to form a right angle
R
Use the diagram at the right for Exercises 2 and 3.
2. AB bisects
A
.
3. RS is a bisector of
8
S
.
5 8
5
B
Vocabulary Builder
transversal
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
transversal (noun) trans VUR sul
I
m
Definition: A transversal is a line that intersects two or more
coplanar lines at distinct points.
t
Main Idea: If three (or more) parallel lines cut off congruent
segments on one transversal, then they cut off congruent segments
on every transversal.
Use Your Vocabulary
4. Underline the correct word(s) to complete the sentence.
A transversal intersects / is parallel to two or more coplanar lines.
Use the diagram at the right for Exercises 5 and 6.
q
5. Circle the transversal(s).
p
q
r
r
t
6. Draw another transversal. Label it s.
t
p
Complete each sentence with the number of angles formed.
7. A transversal that intersects two lines forms
angles.
8. A transversal that intersects four lines forms
angles.
321
Lesson 6-2, Part 2
Theorems 6-6 and 6-7
A
Theorem 6-6 If a quadrilateral is a parallelogram, then its diagonals bisect each other.
9. Use the diagram at the right. If ABCD is a ~, then AE 5
and BE >
E
.
D
Theorem 6-7 If three (or more) parallel lines cut off congruent segments on one
transversal, then they cut off congruent segments on every transversal.
Use the diagram at the right for Exercises 10 and 11.
* ) * ) * )
10. If AB 6 CD 6 EF and AC > CE, then BD >
A
.
C
B
D
C
11. Mark the diagram to show your answer to Exercise 10.
B
F
E
Problem 3 Using Algebra to Find Lengths
Got It? Find the values of x and y in ~PQRS at the right. What are PR and SQ?
P
3y 12. Circle the reason PT > TR and ST > TQ.
Diagonals of a
parallelogram
bisect each other.
1
Opposite sides of
a parallelogram
are congruent.
PR is the
perpendicular
bisector of QS.
S
Q
7
x T
y
2x
R
13. Cross out the equation that is NOT true.
y5x11
3y 2 7 5 x 1 1
3y 2 7 5 2x
14. Find the value of x.
15. Find the value of y.
16. Find PT.
17. Find ST.
PT 5 3 (
5
)27
ST 5
27
11
5
5
18. Find PR.
PR 5 2(
19. Find SQ.
SQ 5 2(
)
5
)
5
20. Explain why you do not need to find TR and TQ after finding PT and ST.
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_______________________________________________________________________
Chapter 6
322
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3(x 1 1) 2 7 5 2x
Problem 4 Using Parallel Lines and Transversals
* ) * ) * ) * )
Got It? In the figure at the right, AE n BF n CG n DH . If EF 5 FG 5 GH 5 6
21. You know that the parallel lines cut off congruent segments on transversal
22. By Theorem 6-7, the parallel lines also cut off congruent segments on
23. AD 5 AB 1 BC 1
24. AB 5
B
A
and AD 5 15, what is CD?
.
E
F
.
C
G
by the Segment Addition Postulate.
5 CD, so AD 5
? CD. Then CD 5
25. You know that AD 5 15, so CD 5
? 15 5
D
H
? AD.
.
Lesson Check • Do you UNDERSTAND?
Error Analysis Your classmate says that QV 5 10. Explain why the
statement may not be correct.
P
Q
S 5 cm
R
T
26. Place a ✓ in the box if you are given the information. Place an ✗ if you
are not given the information.
V
three lines cut by two transversals
three parallel lines cut by two transversals
congruent segments on one transversal
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
27. What needs to be true for QV to equal 10?
_______________________________________________________________________
28. Explain why your classmate’s statement may not be correct.
_______________________________________________________________________
_______________________________________________________________________
Math Success
Check off the vocabulary words that you understand.
parallelogram
opposite sides
opposite angles
consecutive angles
Rate how well you understand parallelograms.
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review
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2
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6
8
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get it!
10
323
Lesson 6-2, Part 2