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.)
19 1. BC plane M
2. BCA and BCD are right angles.
3. BCA BCD
4. −−
AB −−
DB
5. −−
BC −−
BC
6. BCA BCD (HL HL)
7. BAC BDC (CPCTC)
11-3 Parallel Lines and
Planes
(pages 259–260)
1 Parallel
2 Perpendicular
3 Perpendicular
4 Parallel
5 Parallel
6 Parallel
7 Parallel
8 Infinitely many
9 None
10 One
11 Line a is parallel to plane M. Line b is contained
in plane R. Line b is in plane M. Lines
a and b are coplanar and do not intersect.
Therefore, a b.
12 True
13 True
14 True
15 False
16 False
17 True
18 False
19 False
20 True
21 True
22 True
23 True
24 True
25 True
26 False
27 False
28 False
29 False
30 True
11-4 Surface Area of
a Prism
(pages 264–265)
1 (3) 80
2 a 104 b 108 c 224
3 4 faces, 7 edges, 4 vertices
4 5 faces
5 Right prism
6 a 404 cm 2 b 223 ft 2
7 208
8 242 square inches
9 588
10 435 in. 2
11 Lateral area: 255 cm 2 ; total area:
25 √ 3
255 _ 2
c m
2
12 Lateral area: 45 cm 2 ; total area:
9 √ 3
45 _ 2
c m
2
13 144 32 √ 3 cm 2
14 3,880 in. 2
15 Lateral area: 72; total area: 72 12 √ 3
16 Lateral area: 510 square inches; total area:
510 75 √ 3 square inches
17 3 √ 3 in.
18 d 2 h 2 (AB) 2 , but (AB) 2 l 2 w 2 . By substitution,
d 2 h 2 l 2 w 2
11-5 Symmetry Planes
(pages 267–268)
1 (1) A
2 (2) E
3 (1) F
Exercises 4–7: Check students’ sketches.
8 7 symmetry planes
9 Check students’ sketches.
10 112.5 √ 3
11-5 Symmetry Planes 69