Preparing for the Regents Examination Geometry, AK

27 40, 50
28 70, 110
29 20, 35
30 16, 20, 24
31 length 28, width 49
32 45, 135
33 a 8 b 6 c 10
34 a 20 b 9
12-2 Proportions Involving
Line Segments
(pages 298–300)
1 a–d are all true
2 2 _
5 4 _ Proportions are not true, lines not
8
parallel.
3 6
4 28
5 5.4
6 6
7 24
8 5
9 ac _
b
10 np
_
m
11 6
12 20
c(a b)
13 _
a
14 No
15 No
16 No
17 No
18 Yes
19 12
20 1 : 3 or 1 _
3
21 11 cm
22 x 6, AB 47, DE 17, AC 34, EC 9,
BE 9, AD 23.5, DB 23.5
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.)
23 a 1. ABC
2. P is the midpoint of −−
AB .
3. Q is the midpoint of −−
BC .
4. −−
PQ −−
AC (A line joining the midpoints
of two sides of a triangle is
parallel to the third side.)
5. −−
PQ ___
AR
6. R is the midpoint of −−
AC .
7. −−
AB −−−
RQ
8. −−
AP −−−
RQ
9. PQRA is a parallelogram. (Definition
of a parallelogram)
b 30
24 1. ABC, ADC
2. −− wx −−
AC (A line dividing two
sides of a triangle proportionally
is parallel to
the third side.)
3. −− zy −−
AC
4. −− wx −− zy
5. BAD, BCD
6. −− wz −−
BD
7. −− xy −−
BD
8. −− wz −− xy
9. wxyz is a ( Definition of a
parallelogram. parallelogram)
25 48 √ 3
12-3 Similar Polygons
(pages 302–303)
1 1 : 1
2 4, 4.5, 5
3 1 : 4
4 45, 55
5 a 2 : 3
b 4.5, 7.5
c 18
6 9, 13.5, 18
7 5a, 5b, 5c
8 All corresponding angles are congruent, all
corresponding sides are in proportion, 1 : 2.
9 w _ ,
3 x _ ,
3 y
_ ,
3 z _
3
10 32, 40
11 mR mQ 110
12 mI 40; mK 160
13 12
12-3 Similar Polygons 73