Preparing for the Regents Examination Geometry, AK

1 1. −−−−
ABCD
2. 1 2
3. ___
AF −−
DE
4. −−
AC −−
BD
5. AC BD
6. BC BC (Reflexive property)
7. AC BC BD BC
8. AB CD
9. −−
AB −−−
CD
10. ABF DCE (SAS SAS)
2 1. −−−
ABC , −−−
DEF
2. 3 4
3. −−
BF −−
EC
4. 1 2
5. −−−
FBC −−−
CEF (If two angles are
congruent, their
supplements are
congruent.)
6. BCF EFL (ASA ASA)
3 1. −−
BE is a median to −−
FD .
2. −−
FE −−
DE
3. −−
BE −−
BE
4. −−−
AD −−
CF
5. −−
AB −−
CB
6. AD AB CF CB
7. −−
BD −−
BF
8. FBE DBE (SSS SSS)
4 1. −−
AE −−−
DC
2. −−
DE −−
DE
3. AE DE DC DE
4. −−−
AD −−
EC
5. 3 4
6. ADB and 3 are linear pairs.
7. ADB and 3 are supplements.
8. CEB and 4 are linear pairs.
9. CEB and 4 are supplements.
10. ADB CEB
11. 1 2
12. ADB CEB (ASA ASA)
5 1. D is the midpoint of −−
AB .
2. AD DB
3. −−−
AD −−
DB
4. −−
AC −−
BC
5. −−−
DC −−−
DC
6. ADC BDC (SSS SSS)
6 1. −−
AB −−
BC
2. −−
EF −−
AB
3. −−
EF −−
BC
16 Chapter 4: Congruence of Lines, Angles, and Triangles
4. −−
BE bisects −−
CF at D.
5. −−−
CD −−
DF
6. 1 2
7. BCD EFD (SAS SAS)
7 1. −−
AC −−
BD
2. −−
BC −−
BC
3. AC BC BD BC
4. −−
AB −−−
DC
5. 3 4
6. 3 and FBA are linear pairs.
7. 3 and FBA are supplements.
8. 4 and ECD are linear pairs.
9. 4 and ECD are supplements.
10. FBA ECD
11. 1 2
12. EDC FAB (ASA ASA)
8 1. EG is the perpendicular bisector of −−
AB .
2. −−
AF −−
BF
3. EFA is a right angle.
4. EFB is a right angle.
5. EFA EFB
6. mEFA m1 mEFB m1
7. 1 2
8. mEFA m1 mEFB m2
9. DFA CFB
10. −−
DF −−
CF
11. ADF BCF (SAS SAS)
Chapter Review (pages 68–69)
1 Given: ABC and DBE are vertical angles.
PQR ABC
Prove: PQR DBE
2 Given: AB and CD intersect at E.
AEC FGH
Prove: CEB is supplementary to FGH.
3 Given: AEB and CED are perpendicular lines.
Prove: AEC AED
4 Given: AEB and CED are perpendicular lines.
F is not on CD .
Prove: FE is not perpendicular to AB .
5 Since E is the midpoint of −−
AB , CD is a bisector
of −−
AB . Since AEC BEC and they are
a linear pair, the measure of each must be
180 _ 90.
2