Preparing for the Regents Examination Geometry, AK

1 1. −−
AB −−−
CD
2. −−
BC −−−
DA
3. −−
AC −−
AC
4. ABC CDA (SSS SSS)
5. BAC DCA (Corresponding
parts of congruent
triangles are
congruent.)
2 1. −−
BA −−
BC
2. −−−
DA −−−
DC
3. −−
DB −−
DB
4. ABD CBD (SSS SSS)
5. ABC CBD (Corresponding
parts of congruent
triangles are
congruent.)
3 1. 1 3
2. 2 4
3. −−
AC −−
AC
4. DAC BCA (ASA ASA)
5. −−−
AD −−
CB (Corresponding
parts of congruent
triangles are
congruent.)
4 1. −−−
CD is the median drawn from C.
2. −−−
AD −−
DB
3. −−−
CD −−
AB
4. ADC is a right angle.
5. BCD is a right angle.
6. ADC BDC
7. −−−
CD −−−
CD
8. ADC BDC (SAS SAS)
9. −−
CA −−
CB
(Corresponding
parts of congruent
triangles are
congruent.)
5 RS RS
4x 1 3x 3
x 4
RT RT x 6 4 6 10
6 AD CB
2x 5 3x 7
x 12
AB x 10 12 10 22
CD AB 22
AD 2x 5 2(12) 5 29
CB 3x 7 3(12) 7 29
7 The triangle is isosceles and RS RT.
6x 4 3x 11
x 5
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.)
8 1. 1 3
2. 2 4
3. −−
AB −−−
CD
4. ABE CDE (ASA ASA)
5. −−
AE −−
CE
6. −−
BD bisects −−
AC .
7. −−
BE −−
DE
8. −−
AC bisects −−
BD . (Definition of a
bisector)
9 1. −−−
DA bisects BDF.
2. FDA BDA
3. 1 2
4. m1 mFDA m2 mFDA
5. m1 mFDA m2 mBDA
6. EDA CDA
7. −−−
CD −−
DE
8. −−−
AD −−−
AD
9. EDA CDA (SAS SAS)
10. −−
AE −−
AC (Corresponding
parts of congruent
triangles are
congruent.)
10 1. −−
BA is a median of CBF.
2. −−
CA −−
FA
3. −−−
CD −−
FE
4. −−
FC −−−
CD
5. −−
FC −−
EF
6. DCA is a right angle.
7. EFA is a right angle.
8. DCA EFA
9. DCA EFA (SAS SAS)
10. −−−
DA −−
EA (Corresponding
parts of congruent
triangles are
congruent.)
5-2 Using Congruent Triangles to Prove Line Segments Congruent and Angles Congruent 19