Preparing for the Regents Examination Geometry, AK

8. GEA GHA
9. GEA GBC
10. GHA GBC
11. HAG BCG
12-5 Dilations
(pages 310–311)
1 a 10 _
80
b
3
_ c 9
3
2 a BC 10, PA 2.2, BA 11, PS 9.6
b 10 _ 5
8 _
4
3 (21, 9)
4 (6, 12)
5 (9, 0)
6 (27, 3)
7 (12, 12)
8 (10, 36)
9 (20, 12)
10 (2.5, 1)
11 (4, 2)
12 (3, 0)
13 (3, 3.5)
14 (2 √ 2 , 2.5)
15 (16, 8)
16 (10, 2)
17 (15, 0)
18 (3, 15)
19 (3, 2)
20 (4, 8)
21 D 2 r x-axis
22 D 3 r y-axis
23 r x-axis D 1 _
2
24 r x-axis D 1 _
4
25 a A(0, 0), B(12, 0), C(15, 6), D(3, 6)
b Slope AB 0; slope BC 2; slope CD 0;
slope DA 2
c Midpoint M (2.5, 1) and midpoint
M (7.5, 3). Yes, M is the image result
of D 3 operating on point M. Midpoints are
preserved under dilation.
12-6 Proving Proportional
Relationships Among
Segments Related to
Triangles
(pages 315–316)
1 3 : 4 and 3 : 4
2 5 cm
3 4 : 9
4 11 in.
5 AD 6, DC 8
6 18
7 15
8 4 : 7
9 AC 23, PR 8
10 RQ 6, BC 12.2, AC 20.6
11 13
12 19 _ or 4.75
4
13 22
14 12
15 a 4 : 7 b 16 and 20
c 84 and 48 d 48 _
4
84 _
7
16 a BQ 8, QR 5, PR 8 b 36
12-7 Using Similar Triangles
to Prove Proportions
or to Prove a Product
(pages 319–321)
1 128
2 40
3 108
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.)
4 a 1. −−
ED −−
AC and −−
AB −−
CB
2. EDA and ABC are right angles.
3. EDA ABC
12-7 Using Similar Triangles to Prove Proportions or to Prove a Product 75