Download Properties of Parallelograms

6-2
PART 1
Properties of
Parallelograms
Vocabulary
Review
1. Supplementary angles are two angles whose measures sum to
.
2. Suppose /X and /Y are supplementary. If m/X 5 75, then m/Y 5
.
B
A 60í
Underline the correct word to complete each sentence.
3. A linear pair is complementary / supplementary .
E
4. /AFB and /EFD at the right are complementary / supplementary .
C
F
120í
D
Vocabulary Builder
consecutive (adjective) kun SEK yoo tiv
Definition: Consecutive items follow one after another in uninterrupted order.
Examples: The numbers 23, 22, 21, 0, 1, 2, 3, . . . are consecutive integers.
Non-Example: The letters A, B, C, F, P, . . . are NOT consecutive letters of
the alphabet.
Use Your Vocabulary
A
Use the diagram at the right. Draw a line from each angle in Column A
to a consecutive angle in Column B.
Column A
F
Column B
5. /A
/F
6. /C
/E
7. /D
/D
,
9. December, November, October, September,
Chapter 6
C
E
Write the next two consecutive months in each sequence.
8. January, February, March, April,
,
318
B
D
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Math Usage: Consecutive angles of a polygon share a common side.
Theorems 6-3, 6-4, and 6-5
Theorem 6-3 If a quadrilateral is a parallelogram, then its opposite sides are congruent.
Theorem 6-4 If a quadrilateral is a parallelogram, then its consecutive angles are
supplementary.
Theorem 6-5 If a quadrilateral is a parallelogram, then its opposite angles are congruent.
B
Use the diagram at the right for Exercises 10 and 11.
C
10. Mark parallelogram ABCD to model Theorem 6-3 and Theorem 6-5.
A
11. Circle the angle pairs that are supplementary.
/A and /B
/A and /C
/B and /C
D
/A and /D
/B and /D
/C and /D
Problem 1 Using Consecutive Angles
Q
Got It? Suppose you adjust the lamp so that mlS 5 86. What is mlR
in ~PQRS?
P
Underline the correct word or number to complete each statement.
12. /R and /S are adjacent / consecutive angles, so they are supplementary.
64
13. m/R 1 m/S 5 90 / 180
R
S
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14. Now find m/R.
15. m/R 5
.
Problem 2 Using Properties of Parallelograms in a Proof
K
Got It? Use the diagram at the right.
Given: ~ABCD, AK > MK
Prove: /BCD > /CMD
16. Circle the classification of nAKM .
equilateral
isosceles
right
B
A
C
D
M
17. Complete the proof. The reasons are given.
Statements
1)
AK >
Reasons
1) Given
2) /DAB >
2) Angles opposite congruent sides of a triangle are congruent.
3) /BCD >
3) Opposite angles of a parallelogram are congruent.
4) /BCD >
4) Transitive Property of Congruence
319
Lesson 6-2, Part 1
Lesson Check • Do you know HOW?
Use the diagram of ~ABCD to find the value of x.
B
18. What do you know about the lengths of AB and CD? Explain.
__________________________________________________________
C
127 x2
A
2x 3
D
__________________________________________________________
__________________________________________________________
19. Use the expressions for the lengths of AB and CD to write an equation.
20. Use your equation from Exercise 19 to find the value of x.
21. The value of x is
.
Reasoning If you know one angle measure of a parallelogram,
how do you find the other three angle measures? Explain.
Underline the correct word to complete each sentence.
22. If a quadrilateral is a parallelogram, then its consecutive angles are
complementary / supplementary .
23. If a quadrilateral is parallelogram, then its consecutive / opposite angles
are congruent.
24. Look at ~QRST at the right. Suppose you know m/Q. Explain
how you can find the other three angle measures.
__________________________________________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
Chapter 6
320
R
Q
S
T
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Lesson Check • Do you UNDERSTAND?