Preparing for the Regents Examination Geometry, AK

12 a mx 45, my 45
b mx 98, my 82
c mx 60, my 70
d mx 65, my 52
e mx 67, my 78
f mx 15, my 55
g mx 55, my 62.5
13 a 5 b 20 c 35
d 594 e
n 3 _
2
14 102 sides
15 8 sides
16 14 sides
17 6 sides
18 a mx 85
b my 55
19 mD 45
20 m1 m2 25
21 m1 140
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.)
22 1. 6 4
2. x y
3. x z
4. y z (Transitive postulate)
23 1. 2 4
2. 1 3
3. 1 2 3 4
4. m r (Corresponding angles are
congruent.)
24 1. ___
QR ___
PS
2. QPS QRS
3. RPS QRP
4. QPS RPS QRS QRP
or QRP SRP
5. ___
QP ___
RS (Corresponding angles are
congruent.)
25 1. ___
BC bisects ABD.
2. 2 3
3. 1 2
4. 1 3 (Transitive postulate)
5. 5 1
54 Chapter 9: Parallel Lines
6. 3 5
7. a b (Alternate interior angles are
congruent.)
26 1. ___
AC bisects BCD.
2. 3 4
3. ___
AB ___
BC
4. ABC is a right angle.
5. ___
CD ___
AD
6. CDA is a right angle.
7. ___
AC ___
AC
8. I II (Hypotenuse–acute
angle)
27 1. ABCD
2. ___
CF ___
DE
3. ACF BDE
4. ___
CF ___
DE
5. ___
AB ___
CD
6. ___
AB ___
BC ___
CD ___
BC
7. ___
AC ___
BD
8. ACF BDE (SAS SAS)
9. ___
AF ___
BE
28 1. ___
BE bisects ABC.
2. DBE EBA
3. ___
DE ___
BA
4. DEB EBA (Alternate interior
angles are congruent.)
5. DEB DBE (Transitive postulate)
6. ___
DB ___
DE
7. BDE is isosceles. (Definition of
isosceles triangle)
29 1. ___
AF
2. ___
AB ___
CD
3. ___
AC ___
EF
4. ___
AC ___
CE ___
EF ___
CE
5. ___
AE ___
CF
6. ___
AB ___
CD
7. BAE DCF (Corresponding angles
are congruent.)
8. BAE DCF (SAS SAS)
9. ___
BE ___
DF (CPCTC)
30 1. ___
AB ___
CB
2. A C
3. B B
4. ABE CBD (ASA ASA)
5. ___
AE ___
CD
31 1. ___
BA ___
AE
2. BAE is a right angle.
3. 1 2
4. B D