Chapter 13 (PDF)
Chapter 13 (PDF)
Chapter 13 (PDF)
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
5. A DCE 5. Transitivity<br />
6. AB CE 6. Converse of CA<br />
Postulate<br />
7. ABD CED 7. CA Postulate<br />
8. AB BD 8. Given<br />
9. ABD is a right 9. Definition of<br />
angle perpendicular<br />
10. CED is a right 10. Definition of right<br />
angle angle, transitivity<br />
11. BD CE 11. Definition of<br />
perpendicular<br />
LESSON <strong>13</strong>.4 • Quadrilateral Proofs<br />
Proofs may vary.<br />
1. Given: ABCD is a<br />
parallelogram<br />
Show: AC and BD bisect<br />
each other at M<br />
Flowchart Proof<br />
BDC DBA<br />
AIA Theorem<br />
DM BM<br />
CPCTC<br />
ABCD is a<br />
parallelogram<br />
Given<br />
AB CD<br />
Definition of<br />
parallelogram<br />
CAB ACD<br />
AIA Theorem<br />
ABM CDM<br />
ASA Postulate<br />
2. Given: DM BM,<br />
AM CM<br />
Show: ABCD is a<br />
parallelogram<br />
Proof:<br />
A<br />
M<br />
Statement Reason<br />
1. DM BM 1. Given<br />
2. DM BM 2. Definition of<br />
congruence<br />
A<br />
AC and BD bisect<br />
each other at M<br />
Definition of bisect,<br />
definition of congruence<br />
D C<br />
M<br />
CD AB<br />
AM CM<br />
CPCTC<br />
B<br />
Opposite Sides<br />
Theorem<br />
D C<br />
B<br />
3. AM CM 3. Given<br />
4. AM CM 4. Definition of<br />
congruence<br />
5. DMA BMC 5. VA Theorem<br />
6. AMD CMB 6. SAS Postulate<br />
7. DAC BCA 7. CPCTC<br />
8. AD BC 8. Converse of AIA<br />
Theorem<br />
9. DMC BMA 9. VA Theorem<br />
10. DMC BMA 10. SAS Postulate<br />
11. CDB ABD 11. CPCTC<br />
12. DC AB 12. Converse of AIA<br />
Theorem<br />
<strong>13</strong>. ABCD is a <strong>13</strong>. Definition of<br />
parallelogram parallelogram<br />
3. Given: ABCD is a rhombus<br />
Show: AC and BD bisect<br />
each other at M and<br />
AC BD<br />
Flowchart Proof<br />
ABCD is a<br />
parallelogram<br />
Definition of<br />
rhombus<br />
AC and BD bisect<br />
each other<br />
Parallelogram<br />
Diagonals Theorem<br />
AMD and AMB<br />
are supplementary<br />
Linear Pair Postulate<br />
ABCD is a<br />
rhombus<br />
Given<br />
DAM BAM<br />
Rhombus Angles<br />
Theorem<br />
ADM ABM<br />
SAS Postulate<br />
AMD AMB<br />
CPCTC<br />
AMB is a right<br />
angle<br />
Congruent and<br />
Supplementary<br />
Theorem<br />
AC BD<br />
Definition of<br />
perpendicular<br />
A<br />
D C<br />
M<br />
B<br />
AD AB<br />
Definition of<br />
rhombus<br />
AM AM<br />
Reflexive property<br />
Discovering Geometry Practice Your Skills ANSWERS 115<br />
©2008 Kendall Hunt Publishing
Change language