Complete the paragraph proof by filling in the blanks with the appropriate letter from the chart below. A. The definition of a B. The definition of a C. The definition of a parallelogram E. Opposite sides of parallelogram are congruent J. D. The definition of perpendicular lines rhombus right angle F. Diagonals of a parallelogram bisect each other G. Opposite angles of a H. The reflexive property of congruence I. The transitive SSS property of congruence parallelogram are congruent. L. ASA K. SAS М. HL N. AAS Р. СРСТС Given: ABCD is a rhombus B Prove: AC 1 BD ABCD is a rhombus. We know that AB BC by PB PB by ABCD is a parallelogram and we know that AP = PC because ZAPB ZCPB by So, AAPB ACPB by| ZAPB LCPB also form a linear pair and are supplementary. If two congruent angles are supplementary, they must each measure 90°. Therefore, ZAPB is a right angle by and AC 1 BD by
Complete the paragraph proof by filling in the blanks with the appropriate letter from the chart below. A. The definition of a B. The definition of a C. The definition of a parallelogram E. Opposite sides of parallelogram are congruent J. D. The definition of perpendicular lines rhombus right angle F. Diagonals of a parallelogram bisect each other G. Opposite angles of a H. The reflexive property of congruence I. The transitive SSS property of congruence parallelogram are congruent. L. ASA K. SAS М. HL N. AAS Р. СРСТС Given: ABCD is a rhombus B Prove: AC 1 BD ABCD is a rhombus. We know that AB BC by PB PB by ABCD is a parallelogram and we know that AP = PC because ZAPB ZCPB by So, AAPB ACPB by| ZAPB LCPB also form a linear pair and are supplementary. If two congruent angles are supplementary, they must each measure 90°. Therefore, ZAPB is a right angle by and AC 1 BD by
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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Complete the paragraph proof by filling in the blanks with the appropriate letter from the chart below.
![Complete the paragraph proof by filling in the blanks with the appropriate letter from the chart below.
E. Opposite sides of
a parallelogram
are congruent
J. SSS
A. The definition of a B. The definition of a | C. The definition of a D. The definition of
parallelogram
rhombus
right angle
perpendicular
lines
I. The transitive
property of
congruence
F. Diagonals of a
parallelogram
bisect each other
G. Opposite angles
of a
H. The reflexive
property of
parallelogram are
congruent.
L. ASA
congruence
K. SAS
М. HL
N. AAS
Р. СРСТС
Given: ABCD is a rhombus
B
Prove: AC 1 BD
D
ABCD is a rhombus. We know that AB = BC by
РВ РВ by
ABCD is a parallelogram and we know that AP = PC because
ZAPB= ZCPB by
So, ДАРВ ДСРВby
ZAPBE ZCPB also form a linear pair and are supplementary. If two
congruent angles are supplementary, they must each measure 90°. Therefore, ZAPB is a right angle by
and AC I BD by](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b92dbc3-c30f-42ce-8c69-c613ddb13bfd%2Fbc651d17-776d-49ce-9591-c66b442d71bf%2F8esfcys_processed.png&w=3840&q=75)
Transcribed Image Text:Complete the paragraph proof by filling in the blanks with the appropriate letter from the chart below.
E. Opposite sides of
a parallelogram
are congruent
J. SSS
A. The definition of a B. The definition of a | C. The definition of a D. The definition of
parallelogram
rhombus
right angle
perpendicular
lines
I. The transitive
property of
congruence
F. Diagonals of a
parallelogram
bisect each other
G. Opposite angles
of a
H. The reflexive
property of
parallelogram are
congruent.
L. ASA
congruence
K. SAS
М. HL
N. AAS
Р. СРСТС
Given: ABCD is a rhombus
B
Prove: AC 1 BD
D
ABCD is a rhombus. We know that AB = BC by
РВ РВ by
ABCD is a parallelogram and we know that AP = PC because
ZAPB= ZCPB by
So, ДАРВ ДСРВby
ZAPBE ZCPB also form a linear pair and are supplementary. If two
congruent angles are supplementary, they must each measure 90°. Therefore, ZAPB is a right angle by
and AC I BD by
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