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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7. −−−<br />
MR −−<br />
TX (Transitive<br />
postulate)<br />
8. XTS MXT (Alternate<br />
interior angles)<br />
9. MXT MQT (Opposite<br />
angles)<br />
10. MQT RMX (Corresponding<br />
angles)<br />
11. XTS RMX (Transitive<br />
postulate)<br />
12. XST RXM (Corresponding<br />
angles are<br />
congruent)<br />
13. MRX TXS (AAS AAS)<br />
15 1. Parallelogram ABCD<br />
2. X is <strong>the</strong> midpoint of −−<br />
BC .<br />
3. XC 1 _ BC ( Definition of a<br />
2<br />
midpoint)<br />
4. Y is <strong>the</strong> midpoint of −−−<br />
AD .<br />
5. AY 1 _ AD<br />
2<br />
6. −−−<br />
AD −−<br />
BC<br />
7. AD BC<br />
8. 1 _ AD <br />
2 1 _ BC<br />
2<br />
9. AY XC<br />
10. −−<br />
AY −−<br />
XC<br />
11. AMY CMX (Vertical angles<br />
are congruent.)<br />
12. MAY MCX (Alternate interior<br />
angles are<br />
congruent.)<br />
13. MAY MCX (AAS AAS)<br />
14. −−−<br />
XM −−−<br />
YM (CPCTC)<br />
15. a M is <strong>the</strong> midpoint (Definition of<br />
of −−<br />
XY . midpoint)<br />
16. −−−<br />
AM −−−<br />
MC (CPCTC)<br />
17. b M is <strong>the</strong> midpoint (Definition of<br />
of −−<br />
AC . midpoint)<br />
16 1. −−<br />
AC is a diagonal in parallelogram ABCD.<br />
2. −−<br />
AF −−<br />
CE<br />
3. −−<br />
FE −−<br />
FE<br />
4. −−<br />
AF −−<br />
FE −−<br />
CE −−<br />
FE<br />
5. −−<br />
AE −−<br />
CF<br />
6. DAC BCD (Definition of a<br />
parallelogram)<br />
7. BAF DCE (Alternate interior<br />
angles are<br />
congruent.)<br />
8. EAD FBC (Subtraction<br />
postulate)<br />
9. −−−<br />
AD −−<br />
BC (Opposite sides of a<br />
parallelogram are<br />
congruent.)<br />
10. ADE BCF (SAS SAS)<br />
11. AED CFB (CPCTC)<br />
12. −−<br />
DE −−<br />
BF (Alternate interior<br />
angles are congruent.)<br />
17 1. ABCD is a parallelogram.<br />
2. −−<br />
DE −−<br />
AF<br />
3. −−<br />
CF −−<br />
AF<br />
4. DAE and CFB are right angles.<br />
5. DAE CFB<br />
6. −−<br />
CA −−−<br />
AD<br />
7. −−−−<br />
AEBF<br />
8. −−<br />
EB −−<br />
EB<br />
9. −−<br />
AE −−<br />
BF (Subtraction<br />
postulate)<br />
10. DEA CFB (SAS SAS)<br />
11. −−<br />
DE −−<br />
CF (CPCTC)<br />
18 1. Parallelogram ABCD<br />
2. H is <strong>the</strong> midpoint of −−<br />
AB .<br />
3. AH 1 _ AB<br />
2<br />
4. F is <strong>the</strong> midpoint of −−−<br />
DC .<br />
5. FC 1 _ DC<br />
2<br />
6. −−<br />
AB −−−<br />
DC (Opposite sides of a<br />
parallelogram are<br />
congruent.)<br />
7. AB DC<br />
8. 1 _ AB <br />
2 1 _ DC<br />
2<br />
9. AH FC<br />
10. −−−<br />
AH −−<br />
FC<br />
11. −−−<br />
HG −−<br />
AC , −−<br />
FE −−<br />
AC<br />
12. HGA and FEC are right angles.<br />
13. HFA FEC<br />
14. −−<br />
AB −−−<br />
DC<br />
15. CAB ACD<br />
16. GAH ECF (AAS AAS)<br />
17. −−−<br />
HG −−<br />
FE<br />
19 1. Parallelogram ABCD<br />
2. −−<br />
AR −−−<br />
CM<br />
3. −−<br />
AR −−−<br />
MR −−−<br />
CM −−−<br />
MR<br />
4. −−−<br />
AM −−<br />
CR<br />
5. −−−<br />
AD −−<br />
BC<br />
6. −−−<br />
AD −−<br />
BC<br />
10-2 The Parralallogram 57
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