Preparing for the Regents Examination Geometry, AK

5. RSQ TSV (Vertical angles)
6. QRS VTS (AAS AAS)
7. −−−
QR −−
PT (CPCTC)
8. −−
PT −−
TV
9. −−−
QR −−
PT
10. −−−
QR −−
PT
11. PQRT is a ( One pair of opparallelogram.
posite sides is both
congruent and
parallel.)
13 1. Parallelogram ABCD
2. −−−
DC −−
AB (Opposite sides of
a parallelogram are
congruent.)
3. −−
DF −−
BE
4. −−−−
DFEB
5. CDF ABE (Alternate interior
angles are congruent.)
6. DFC BEA (SAS SAS)
7. −−
CF −−
AE (CPCTC)
8. −−−
AD −−
CB (Opposite sides of
a parallelogram are
congruent.)
9. ADF EBA
10. AFD CEB (SAS SAS)
11. −−
AF −−
CE (CPCTC)
12. AECF is a (Both pairs
parallelogram. of opposite sides are
congruent.)
14 1. −−
KJ is a diagonal in parallelogram KBJD.
2. −−
KA −−
JC
3. BJC AKD
4. −−
BJ −−−
KD
5. BJC KAD (SAS SAS)
6. −−
BC −−−
AD (CPCTC)
7. −−
BK −−
JD
8. CJD BKA
9. ABK CDJ (SAS SAS)
10. −−
AB −−−
CD (CPCTC)
11. ABCD is a ( Both pairs
parallelogram. of opposite sides are
congruent.)
15 1. −−
BD is a diagonal in parallelogram
ABCD.
2. BEC AFD
3. EBC ADF (Alternate interior
angles are congruent.)
4. −−
BC AD (Opposites sides of
a parallelogram are
congruent.)
60 Chapter 10: Quadrilaterals
5. CBE AFD
6.
(AAS AAS)
−−
AF −−
EC
7.
(CPCTC)
−−
DF −−
EB
8. ABE FDC
9.
(CPCTC)
−−
AB −−−
DC
10. ABE CDE
11.
(SAS SAS)
−−
EA −−
CF (CPCTC)
10-4 Rectangles
(pages 227–228)
1 (1) are congruent
2 AR DR
3(4x 3) 10x 1
x 5
AR CR DR BR 51
3 AR BR
2(x 6) 3x 20
x 8
AR CR 4
BD 8
4 DR CR
4(3x 10) 3(x 2) 12
x 46 _
9
AR 46 _
9
AC BD 128 _
9
5 AC BD
3(2x 5) 1 _ (4x 4)
4 2 _ (12x 3) 5x
3
x 2
AC 24
DR 12
6 2x 3 0 36
x 3
7 PR QS
4x 3 6x 7
x 5
PR 4(5) 3 23
QS 6(5) 7 23
√ PR QS √ 23 23 23
8 mADB mDAC 90 49 41
9 (5, 6)
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