Preparing for the Regents Examination Geometry, AK

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.)
5 1. −−−−
CMD is a line segment.
2. −−−
CM −−−
MD
3. M is the mid- (Definition of a midpoint)
point of −−−
CD .
6 1. −−−−
ABCD is a line segment.
2. −−
AB −−−
CD
3. BC BC
4. AB CD
5. AB BC CD BC
6. AC BC
7. −−
AC −−
BD (Line segments that are
equal in measure are
congruent.)
7 1. −−
AB −−−
CD
2. AB CD
3. −−
AB and −−−
CD bisect each other at E.
4. AE 1 _ AB
2
5. CE 1 _ CD
2
6. AE CE
7. −−
AE −−
CE (Line segments that are
equal in measure are
congruent.)
8 1. −−
PQ −−−
QR
2. mPQR 90
3. mPQR mABC
4. mABC 90
5. −−
AB −−
BC (Perpendicular lines form
right angles.)
9 1. PQ XY
2. QR YZ
3. PQ QR XY YZ
4. PQ QR PR
5. XY YZ XZ
6. PR XZ
7. −−
PR −−
XZ (Line segments that are
equal in measure are
congruent.)
10 1. DAB and EBA are straight angles.
2. mDAB 180
3. mEBA 180
4. m1 m2
5. mDAB m1 mEBA m2
6. m3 m4 (Substitution postulate)
11 1. −−
AC −−
BC
2. AC BC
4. −−−
DC −−
EC
5. DC EC
6. AD DC BC EC
7. AD BE
8. −−−
AD −−
BE (Line segments that are
equal in measure are
congruent.)
12 1. −−−
AD −−
BC
2. AD BC
3. E is the midpoint of −−−
AD .
4. DE 1 _ AD
2
5. F is the midpoint of −−
BC .
6. BF 1 _ BC
2
7. BF DE
8. −−
BF −−
DE (Line segments that are
equal in measure are
congruent.)
Chapter Review 11