Download Chapter 6 Solutions

Chapter 6 Solutions
Section 6.3
1. (a) 2.5 (b) 7.5 (c) 3 (d) 2.5 (e) 7
2. (a) 69o (b) 75o (c) 45o (d) 5.6 cm
(f) 3.5
(e) 7.6 cm
3. The ratio of the lengths is not equal to the ratio of the widths.
4. (a) The corresponding angles are congruent. The corresponding sides are proportional.
5.
6.
7.
8.
9.
10.
11.
12.
13.
(b) 2 or ½.
(a) F (b) T (c)T
(d)F
(e) T
(a) yes (b) yes (c) yes (d) no
(a) 5.6 (b)11.7 (c) 3 (d) 6
Done
(1) alternate-interior angles formed by the transversal line AC through parallel lines AB and CD.
(2) alternate-interior angles formed by the transversal line BD through parallel lines AB and CD.
(3) Theorem of similarity AA.
done
(1) vertically opposite angles.
(2) ½.
(3) theorem of similarity SAS.
K = 3/2. Triangles are similar by SSS.
(a) AA (b) SAS (c) AA (d) SSS
Section 6.4
1. A)
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
;b) 6.2, 4.3
(a) 8 (b) 13 (c) 4 (d) 2.8
(a) 2.4 cm
(b) 1) 60o
2) 45o
3
6m
24 units
7.5 m
2 cm
A) mSU; b)mPR; c) mQS; d) mQS
A) 3.75; b) 7.8; c) 4
19.2 cm
(b) b’=1.5 c’=4.5
(c) 12; 8; 16
Section 6.4
1. A) x=0.9; y=1.6; z=2
b) z = 7.2; x = 3.24; y = 5.76; h = 4.32
(c) x = 3.78; y =6.72; h = 5.04
(d) y = 2.8; z = 1.26; x = 2.1
e) y = 3.84; h = 2.88; x =3.6; t = 4.8
f) y = 5.12; x = 2.88; z =
4.8
2. A) length BH = 18cm
length CH = 32cm
b) length AB = 30 cm
3. A) h = 2.88 cm; m = 3.84cm; n = 2.16cm b) c=6.75; m=4.05; n=7.2
d) n=8; c=7.5; b=10
4. X=4.8; y=6.4; z=3.6; t=3.84; u=2.88; v=2.16
5.
6. 15.3cm3
length AC = 40 cm
c) c=4.5; b=6;m=2.7
Evaluaton
1. 140o
2. A) ASA b)no c)SAS d) SSS
3. A) SAS b)No c)SSS d)AA
4. 1) common side to both triangles; 2) opposite sides of a parallelogram are congruent; 3) same as
2; 4) Theorem of congruence SSS
5. 54.1
6. 1) vertically opposite angles; 2) alternate-interior angles formed by the transversal line BE
through parallel lines BC and DE; 3) theorem of similarity AA; 4) corresponding sides of two
similar triangles are proportional; 5) 2 cm.
7. 1) any segment parallel to one side in a triangle determines two similar triangles; 2)
corresponding sides of two similar triangles are proportional; 3) 3 cm.
8. 1) the angles at the base of an isosceles triangle are congruent; 2) supplementary angles to two
congruent angles are congruent; 3) by hypothesis; 4) triangle ABC is isosceles SAS; 5)
corresponding elements are congruent; 6) by definition of an isosceles triangle.
9. 25.82
10. 77
11. A) h=1.44; m=1.92; n=1.08; a=3
b) c=13.5; m=8.1; n=14.4; a=22.5
c)a=3.75; b=3;
c=2.25; m=1.35;d)h=2.4; a=5; b=4; c=3 e) c=1.5; h=1.2; b=2; n=1.6