Preparing for the Regents Examination Geometry, AK

18 1. I is the midpoint of −−
EG .
2. −−
EI −−
IG
3. EI IG
4. −−
EG −−
EI −−
IG
5. EG EI IG
6. EG EI EI or EG 2EI
7. EH 2EI
8. EG EH
9. −−
EG −−
EH
10. FGE IEH
11. FEG HIE
12. FGE IEH (ASA ASA)
5-1 Line Segments
Associated With Triangles
(page 71)
1 One line
2 C
Median
CHAPTER
5
A E F D B
Angle Bisector
3 −−
AE and −−
BE
4 −−
AB and −−−
CD
5 ACF and BCF
6 ADC and BDC
Altitude
18 Chapter 5: Congruence Based on Triangles
19 1. AEB, CED are right angles.
2. AEB CED
3. A C
4. −−
AE −−
CE
5. ABC CDE (ASA ASA)
20 1. −−−
DC −−−
AD
2. −−
AB −−−
AD
3. −−−
DC −−
AB
4. −−
DF −−
BE
5. −−
EF −−
EF
6. DF EF BE EF
7. −−
DE −−
BF
8. 1 2
9. ABF DCE (SAS SAS)
Congruence Based on
Triangles
5-2 Using Congruent
Triangles to Prove Line
Segments Congruent and
Angles Congruent
(pages 72–73)
Note: Since there are many variations of proofs,
the following is simply one set of acceptable
statements to complete each proof. Depending
on the textbook used, the wording and format
of reasons may differ, so they have not been
supplied for the method of congruence applied
in each problem. (These solutions are intended
to be used as a guide—other possible solutions
may vary.)