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.)
43 1. −−
TS −−
QP
2. QRP TSR (Corresponding
angles are
congruent.)
3. PQR STR
4. R R
5. PQR STR (AAA AAA)
44 1. −−
AE −−
BC , −−
BD −−
AC
2. FEB and BDC are right angles.
3. FEB BDC
4. FBE FBE
5. BFE BCD (AA)
45 1. −−
AB −−−
CD
2. ABE DCE (Alternate interior
angles are
congruent.)
Geometry of the Circle
13-1 Arcs and Angles
(pages 345–346)
1 a 36 b 51 c 90
d 180 e 2r
2 a BC , CD , AD , BD , AB
b ABC , ADC
c ABD , BDA , ADB
3. BAE CDE
4. AEB CED (Vertical angles are
congruent.)
5. a ABE DCE (AAA AAA)
6. BE _ EC
AE _
ED
7. b BE _
AE
EC _
ED (Corresponding
sides of similar
triangles are in
proportion.)
8. c BE ED (The product of
EC AE means equals
the product of
46 1.
extremes.)
−−
BC −−
AF
2. ECA and FDA are right angles.
3. ECA FDA
4. A A
5. ADF ACB
6. BA _ =
AF _
BC
DF
7. BA DF (The product of
AF DC means equals
the product of
extremes.)
CHAPTER
13
3 RB 105, BS 75, AS 105, AR 75
4 a 155 b 25 c 155 d 335
5 a 296 b 244 c 296 d 244
6 a 73 b 132 c 155 d 180
e 155
i 287
f 228 g 253 h 205
7 a 20 b 60 c 120 d 110
e 7 f 60 g 70 h 120
i 110 j 230 k 240 l 290
13-1 Arcs and Angles 79