Preparing for the Regents Examination Geometry, AK
Preparing for the Regents Examination Geometry, AK
Preparing for the Regents Examination Geometry, AK
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
7. MAD RCB<br />
8. MAD RCB (SAS SAS)<br />
9. −−<br />
BR −−−<br />
DM (CPCTC)<br />
20 1. Parallelogram ABCD<br />
2. −−−<br />
QD bisects D.<br />
3. mCDQ 1 _ mCDP<br />
2<br />
4. −−<br />
PB bisects B.<br />
5. mABP 1 _ mABQ<br />
2<br />
6. CDP ABQ<br />
7. mCDP mABQ<br />
8. 1 _ mCDP <br />
2 1 _ mABQ<br />
2<br />
9. mCDQ mABP<br />
10. CDQ ABP<br />
11. DCQ BAP<br />
12. ABP CDQ (SAS SAS)<br />
13. a −−<br />
AP −−−<br />
CQ (CPCTC)<br />
14. −−<br />
BC −−−<br />
AD<br />
15. b −−<br />
BQ −−<br />
PD (Subtraction<br />
postulate)<br />
21 1. Parallelogram PQRS<br />
2. PS PQ<br />
3. mx mQSP<br />
4. −−−<br />
QR −−<br />
PS<br />
5. y QSP (Alternate<br />
interior angles<br />
are congruent.)<br />
6. my mQSP<br />
7. mx > my (Substitution<br />
postulate)<br />
22 1. Parallelogram MARC<br />
2. AR MA<br />
3. mAMR mARM<br />
4. ARM CMR (Alternate<br />
interior angles<br />
are congruent.)<br />
5. mARM mCMR<br />
6. mAMR mCMR (Substitution<br />
postulate)<br />
7. AMR is not congruent to CMR.<br />
58 Chapter 10: Quadrilaterals<br />
10-3 Proving That a<br />
Quadrilateral Is a<br />
Parallelogram<br />
(pages 224–225)<br />
1 Check students’ answers. The following is<br />
one possible solution.<br />
Slope of −−<br />
AB slope of −−−<br />
CD 3. Slope of<br />
−−−<br />
AD slope of −−<br />
BC 0. Both pairs of opposite<br />
sides are parallel.<br />
2 a PR 5<br />
b ( 7 _ , 8) or (3.5, 8)<br />
2<br />
3 a Check students’ answers. The following is<br />
one possible solution.<br />
DR AB 10. Slope of −−−<br />
DR slope<br />
of −−<br />
AB 0. One pair of opposite sides are<br />
both congruent and parallel.<br />
b The length of <strong>the</strong> altitude from B to −−−<br />
DR<br />
is 5.<br />
Note: Since <strong>the</strong>re are many variations of proofs,<br />
<strong>the</strong> following is simply one set of acceptable<br />
statements to complete each proof. Depending<br />
on <strong>the</strong> textbook used, <strong>the</strong> wording and <strong>for</strong>mat<br />
of reasons may differ, so <strong>the</strong>y have not been<br />
supplied <strong>for</strong> <strong>the</strong> method of congruence applied<br />
in each problem. (These solutions are intended<br />
to be used as a guide—o<strong>the</strong>r possible solutions<br />
may vary.)<br />
4 1. Parallelogram LOVE<br />
2. AOV BEL<br />
3. OAV EBL<br />
4. −−−<br />
OV −−<br />
EL<br />
5. OAV EBL (AAS AAS)<br />
5 BF 1 _ CE (segment connecting midpoints of<br />
2<br />
sides of a triangle) and CD 1 _ CE (defin-<br />
2<br />
tion of midpoint). BF CD. DF 1 _ AC and<br />
2<br />
BC 1 _ AC. BF CD and DF BC. Opposite<br />
2<br />
sides of a parallelogram have equal measure<br />
so <strong>the</strong>y are congruent.<br />
6 1. −−<br />
KL and −−<br />
EU bisect each o<strong>the</strong>r at M.<br />
2. −−−<br />
KM −−−<br />
LM<br />
3. −−−<br />
EM −−−<br />
MU<br />
4. EMK UML<br />
5. EMK UML (SAS SAS)<br />
6. −−<br />
EK −−<br />
LU (CPCTC)<br />
7. K is <strong>the</strong> midpoint of −−<br />
JE .
Change language