Preparing for the Regents Examination Geometry, AK
Preparing for the Regents Examination Geometry, AK
Preparing for the Regents Examination Geometry, AK
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8. EK 1 _ EJ<br />
2<br />
9. L is <strong>the</strong> midpoint of −−−<br />
UN .<br />
10. UL 1 _ UN<br />
2<br />
11. EK UL<br />
12. 1 _ EJ <br />
2 1 _ UN<br />
2<br />
13. EJ UN<br />
14. −−<br />
EJ −−−<br />
UN<br />
15. −−<br />
EU −−<br />
EU<br />
16. LUM KEM<br />
17. EUN UEJ<br />
18. −−<br />
EN −−<br />
UJ<br />
19. JUNE is a ( Both pairs<br />
parallelogram. of opposite sides<br />
are congruent.)<br />
7 1. ABCD is a parallelogram.<br />
2. −−<br />
RC<br />
3. −−−<br />
DQ −−<br />
RC , −−<br />
AR −−<br />
RC<br />
4. DQC and ARB are right angles.<br />
5. DQC ARB<br />
6. RBA QCD (Corresponding<br />
angles are<br />
congruent.)<br />
7. −−<br />
AB −−−<br />
DC (Opposite sides of<br />
a parallelogram are<br />
congruent.)<br />
8. AB DC<br />
9. ARB DQC (AAS AAS)<br />
10. −−<br />
AR −−−<br />
DQ (CPCTC)<br />
11. AR DQ<br />
12. −−<br />
AR −−−<br />
DQ Segments perpendicular<br />
to <strong>the</strong> same<br />
segment are<br />
parallel.)<br />
13. ARQD is a ( One pair of opparallelogram.<br />
posite sides is both<br />
congruent and<br />
parallel.)<br />
8 1. −−<br />
PE bisects −−<br />
HL at M.<br />
2. −−−<br />
HM −−−<br />
ML<br />
3. EPL PEH<br />
4. HME LMP<br />
5. HME LMP (AAS AAS)<br />
6. −−<br />
HE −−<br />
LP<br />
7. −−<br />
HE −−<br />
LP<br />
8. HELP is a ( One pair of opparallelogram.<br />
posite sides is both<br />
congruent and<br />
parallel.)<br />
9 1. Parallelogram ABCD<br />
2. −−−<br />
AD −−<br />
BC<br />
3. −−−<br />
AM −−−<br />
NC<br />
4. M is midpoint of −−−<br />
AD .<br />
5. AM 1 _ AD<br />
2<br />
6. N is <strong>the</strong> midpoint of −−<br />
BC .<br />
7. NC 1 _ BC<br />
2<br />
8. −−−<br />
AD −−<br />
BC<br />
9. AD BC<br />
10. 1 _ AD <br />
2 1 _ BC<br />
2<br />
11. AM NC<br />
12. −−−<br />
AM −−−<br />
NC<br />
13. ANCM is a ( One pair of opparallelogram.<br />
posite sides is both<br />
congruent and<br />
10 1. BR and DM <br />
2. 2 3<br />
3.<br />
parallel.)<br />
−−<br />
BC −−−<br />
AD<br />
4. 1 4<br />
5. BAD DCB (Supplements of<br />
congruent angles<br />
6.<br />
are congruent.)<br />
−−<br />
BD −−<br />
BD<br />
7. BCD DAB<br />
8.<br />
(AAS AAS)<br />
−−<br />
BC −−−<br />
AD<br />
9. ABCD is a ( One pair of opparallelogram.<br />
posite sides is both<br />
congruent and<br />
parallel.)<br />
11 1. −−<br />
QS bisects −−<br />
PR (at M).<br />
2. −−−<br />
QM −−−<br />
MS<br />
3. 1 2<br />
4. QMR SMP<br />
5. QMR SMP<br />
6.<br />
(AAS AAS)<br />
−−−<br />
QR −−<br />
SP<br />
7. −−<br />
PR −−<br />
PR<br />
8. PSR RQP<br />
9.<br />
(SAS SAS)<br />
−−<br />
QP −−<br />
SP<br />
10. PQRS is a ( One pair of opparallelogram.<br />
posite sides is both<br />
congruent and<br />
12 1.<br />
parallel.)<br />
−−−<br />
QV bisects −−<br />
RT .<br />
2. −−<br />
RS −−<br />
ST<br />
3. −−−<br />
QR −−<br />
PV<br />
4. RQS TVS (Alternate interior<br />
angles)<br />
10-3 Proving That a Quadrilateral Is a Paralallogram 59
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