Preparing for the Regents Examination Geometry, AK

Quadrilaterals
10-2 The Parallelogram
(pages 221–223)
1 mP 48, mQ mS 132
2 mR 30, mQ mS 150
3 mQ mR 180
(3x 5) (4x 25) 180
7 x 210
x 30
mS mQ 85
mP mR 95
4 mP mQ 180
(7x 12) (2x 3) 180
9 x 189
x 21
mR 135
mS 45
5 3x 5 1 _
2 (5x 3)
6x 1 0 5x 3
x 7
PR 5(7) 3 32
QS 3(7) 5 16
6 PRS PRQ; QPS SRP; QMP
SMR; QMR SMP
7 x (5x 6) 180
x 31
The angles are 31 and 149.
8 (3x 24) x 180
x 39
The angles are 39 and 141.
9 x 3
10 4
11 mETS mBTE mTEB 42
56 Chapter 10: Quadrilaterals
CHAPTER
10
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.)
12 1. ABCD and DAPQ are parallelograms.
2. −−−
AD ___
BC (Opposite sides of
a parallelogram are
congruent.)
3. −−−
AD −−
PQ (Opposite sides of
a parallelogram are
congruent.)
4. −−
BC −−
PQ (Transitive property)
13 1. ABCD is a parallelogram.
2. −−
BC −−−
AD
3. GBF GDE
4. BGF DGE
5. BG −−−
GD (Diagonals of a parallelogram
bisect
each other.)
6. BFG DEG (ASA ASA)
7. −−
FG −−
GE
8. G is the midpoint ( Definition of
of −−
FE . midpoint)
14 1. −−−
MX −−
QS
2. −−
TX −−−
QM
3. QMXT is a parallelogram.
4. M is the midpoint of −−−
QR .
5. QM −−−
MR
6. QM −−
TX (Opposite sides of
a parallelogram are
congruent.)