Fill in the missing statement and reason of the proof below. Given: ABCD is a parallelogram, ED bisects ZADC and FB bisects ZABC. Prove: AADE ACBF. Step Statement Reason ABCD is a parallelogram ED bisects LADC Given FB bisects LABC ZADC E LABC Opposite angles of a parallelogram are congruent 2. MZADE = }LADC When an angle is bisected, each part is half the measure of the whole angle 3 m/CBF = }LABC When an angle is bisected, each part is half the measure of the whole angle 4 Type of Statement AD BC Opposite sides of a parallelogram are congruent ZA ZC Opposite angles of a parallelogram are congruent AADE ACBF ASA F A. E Note: AB and DC are segments.
Fill in the missing statement and reason of the proof below. Given: ABCD is a parallelogram, ED bisects ZADC and FB bisects ZABC. Prove: AADE ACBF. Step Statement Reason ABCD is a parallelogram ED bisects LADC Given FB bisects LABC ZADC E LABC Opposite angles of a parallelogram are congruent 2. MZADE = }LADC When an angle is bisected, each part is half the measure of the whole angle 3 m/CBF = }LABC When an angle is bisected, each part is half the measure of the whole angle 4 Type of Statement AD BC Opposite sides of a parallelogram are congruent ZA ZC Opposite angles of a parallelogram are congruent AADE ACBF ASA F A. E Note: AB and DC are segments.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Question
What statement and reason for step number 5 will help prove how you got the the 8th step ?
![Fill in the missing statement and reason of the proof below.
Given: ABCD is a parallelogram, ED bisects ZADC and FB bisects LABC.
Prove: AADE ACBF.
Step
Statement
Reason
ABCD is a parallelogram
ED bisects LADC
Given
1
FB bisects ZABC
ZADC E ZABC
Opposite angles of a parallelogram are congruent
mZADE = }LADC
When an angle is bisected, each part is half the measure of the
whole angle
3
When an angle is bisected, each part is half the measure of the
whole angle
m2CBF =
ZABC
4.
Type of Statement
6
AD BC
Opposite sides of a parallelogram are congruent
ZAE ZC
Opposite angles of a parallelogram are congruent
8
AADE = ACBF
ASA
D
F
A.
E
B
Note: AB and DC are segments.
Submit Answer
attempt 2 out of 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe41986f-52ee-4258-92fc-936bf3f6b54e%2F2c215557-37de-423f-99dc-9f6a17ffb460%2Ft947ke2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Fill in the missing statement and reason of the proof below.
Given: ABCD is a parallelogram, ED bisects ZADC and FB bisects LABC.
Prove: AADE ACBF.
Step
Statement
Reason
ABCD is a parallelogram
ED bisects LADC
Given
1
FB bisects ZABC
ZADC E ZABC
Opposite angles of a parallelogram are congruent
mZADE = }LADC
When an angle is bisected, each part is half the measure of the
whole angle
3
When an angle is bisected, each part is half the measure of the
whole angle
m2CBF =
ZABC
4.
Type of Statement
6
AD BC
Opposite sides of a parallelogram are congruent
ZAE ZC
Opposite angles of a parallelogram are congruent
8
AADE = ACBF
ASA
D
F
A.
E
B
Note: AB and DC are segments.
Submit Answer
attempt 2 out of 2
![ZABC
whole angle-
Type of Statement
XY WZ
%3B
6.
Type of Stateme
ZX 설 LY
Opposite angl
8.
ASA
AXYZ ATUV
F
XY WZ
XY 1WZ
Classify a triangle
Classify a quadrilateral
ZX and ZY are
complementary/supplementary
ZX is a right angle
E
XY bisectsZX
AB and DC are segme
XY bisects WZ
XY = WZ (or 2W Z)
Subr
m/X = mZY (or 2m/Y)
5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe41986f-52ee-4258-92fc-936bf3f6b54e%2F2c215557-37de-423f-99dc-9f6a17ffb460%2F689p3h8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:ZABC
whole angle-
Type of Statement
XY WZ
%3B
6.
Type of Stateme
ZX 설 LY
Opposite angl
8.
ASA
AXYZ ATUV
F
XY WZ
XY 1WZ
Classify a triangle
Classify a quadrilateral
ZX and ZY are
complementary/supplementary
ZX is a right angle
E
XY bisectsZX
AB and DC are segme
XY bisects WZ
XY = WZ (or 2W Z)
Subr
m/X = mZY (or 2m/Y)
5
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