Download Practice C

LESSON
NAME _________________________________________________________ DATE ___________
6.4
Practice C
For use with pages 347–355
In the diagram shown, BDEG is a rectangle and ABCD is a
rhombus. Find the measure of the indicated angle.
1. GDB
2. ABC
3. DAB
4. BCG
5. GCE
6. DEG
7. AHB
8. DGB
A
H
B
C
G
D
63
E
Decide whether the statement is true or false. Decide whether
the converse is true or false. If both statements are true, write a
biconditional statement.
9. If a quadrilateral is a rectangle, then it is a parallelogram.
10. If a quadrilateral is a parallelogram, then it is a rhombus.
11. If a quadrilateral is a square, then it is a rhombus.
12. If a quadrilateral is a rectangle, then it is a rhombus.
13. If a rhombus is a square, then it is a rectangle.
Find the length or angle measure.
14. WXYZ is a square.
15. WXYZ is a rhombus.
16. WXYZ is a rectangle.
WX 1 10x
mX 2410 x
Perimeter of XYZ 24
YZ 14 3x
mZ 6x 15
XY YZ 5x 1
XY mY XZ 13 x
?
?
WY ?
Write a two-column or a paragraph proof.
17. Given: WHAT is a parallelogram.
18. Given: GEC GHX
DART is a rhombus.
GEBH is a parallelogram.
Prove: WHAT is a rectangle.
W
Prove: GEBH is a rhombus.
T
C
D
R
G
E
X
Lesson 6.4
H
A
H
19. Given: JANE is a parallelogram.
B
E
P
N
J
X
A
JXPE is a parallelogram.
XPEN
Prove: JANE is a rectangle.
60
Geometry
Chapter 6 Resource Book
Copyright © McDougal Littell Inc.
All rights reserved.
Answer Key
Chapter 6
Lesson
6.4
Practice C
1. 27 2. 54 3. 126 4. 54 5. 126
6. 90 7. 90 8. 63 9. true; false
10. false; true 11. true; false 12. false; false
13. true; true; a rhombus is a square if and only if
it is a rectangle. 14. 11 15. 60 16. 10
17.
Statements
1. WHAT is a .
2. WD DA
3. HD DT
4. DART is a
5.
6.
7.
8.
9.
rhombus.
DT DA
WD HD DA DT
WA WD DA
HT HD DT
WA HT
WHAT is a
rectangle
18.
Statements
Reasons
1. Given
2. Diagonals of bisect
each other.
3. Diagonals of bisect
each other.
4. Given
5. Definition of rhombus
6. Substitution
7. Seg. Add. Postulate
8. Substitution
9. If diagonals of are
, then it is a rectangle.
Reasons
1. GEC GHX 1. Given
2. GE GH
2. Corresp. parts of 3. GEBH is a 3.
4. GH EB
4.
5. GE HB
5.
6. GE EB
6.
7. EB HB
7.
8. GEBH is a
8.
rhombus.
’s are .
Given
If quad. is a , then
opp. sides are .
If quad. is a , then
opp. sides are .
Substitution
Substitution
A with 4 sides
is a rhombus.
19.
Statements
1. JXPE is a .
2. EJ PX,
EP JX
3. EX EX
4. JXE PEX
5. J XPE
Reasons
1. Given
2. Opp. sides of 3.
4.
5.
6. XPEN
6.
7. XPE is a rt. .
7.
8. J is a rt. .
8.
9. JANE is a .
9.
10. J and A are
10.
supplementary.
11. A is a rt. .
11.
12. N and PEJ
12.
are rt. .
13. JANE is a
rectangle.
13.
are .
Reflex. Prop. of SSS Congr. Postulate
Corresp. parts of ’s are .
Given
Definition of Substitution
Given
Adj. of are supplementary.
If 2 are suppl. and
one is a rt. , then
the other is a rt. .
Opp. of a are .
A with 4 rt. is a rectangle.