Answer Key
CHAPTER 6
SIMILAR FIGURES
6.1 SIMILAR POLYGONS
BUILD YOUR SKILLS, P. 257
x = 45 cm
y = 70°
z = 17.5 cm
7. length: 16.25 cm; width: 12 cm; height: 7 cm
1. LP = 7 cm
8. length: 20 in; width: 17.5 in; height: 13.5 in
OP = 6 cm
9. Box 1: 9 cm by 6 cm by 3 cm;
ON = 4 cm
Box 2: 6.75 cm by 4.5 cm by 2.25 cm;
MN = 6 cm
Box 3: 5.1 cm by 3.4 cm by 1.7 cm
2. 22 feet by 12 feet
PRACTISE YOUR NEW SKILLS, P. 262
3. ABCD∼QRST and EFGH∼LKJI
1. 855 cm or 8.55 m
4. Corresponding angles:
2. about 3.1 m and 3.75 m
∠A = ∠G
3. 108°, 204°, 63°, 120°, and 45°
∠B = ∠H
4. 48 mm by 20 mm; 1920 mm by 800 mm
∠C = ∠I
5. Funnel 1: height about 13.3 cm, spout length
∠D = ∠J
∠E = ∠K
∠F = ∠L
Angle measures:
∠D = 73°
about 8.3 cm, spout diameter about 1.7 cm
Funnel 2: height about 10.7 cm, spout length
about 6.7 cm, spout diameter about 1.3 cm
Funnel 3: height 8 cm, spout length 5 cm,
spout diameter 1 cm
∠H = 21°
6.2 DETERMINING IF TWO POLYGONS ARE
SIMILAR
∠E = 40°
BUILD YOUR SKILLS, P. 266
5. ∠B = 100°
∠X = 32°
1. Yes, the two hexagons are similar. If a hexagon
is regular, all the angles are congruent and
all sides are congruent. Therefore, the two
∠C = 48°
6. w = 42°
hexagons Pierre drew will have congruent
corresponding angles, and are similar.
359
360
MathWorks 10 Workbook
2. Yes, the picture and poster are similar.
6.3 DRAWING SIMILAR POLYGONS
3. Zora is correct if she is comparing rectangle
BUILD YOUR SKILLS, P. 272
ABCD to rectangle PQRS. But if Zora compares
the longer sides of the two rectangles, and the
1.
shorter sides of the two rectangles, she will
find that they are similar. She can compare
rectangle ABCD to rectangle QRSP. Since 100
50
is equal to 60 , Zora can say that rectangle
30
ABCD is similar to rectangle QRSP.
4. Yes, it is true that if you increase or decrease
the side lengths of a figure by the same factor,
the resulting figure will be similar to the
original. If you multiply or divide by the same
number, you are keeping the same proportion.
4 cm
8 cm
2. See diagram on the next page
3. 1 in:5.5 ft
4. scale factor: 1.25
5. 26 cm by 15.6 cm by 6.5 cm
6. length: 70 cm; upper portion: 14 cm;
half-width: 35 cm
Examples will vary.
5. The framed picture is not similar to
the original.
PRACTISE YOUR NEW SKILLS, P. 275
1. 75 mm
6. The two cylinders are not similar.
2.
PRACTISE YOUR NEW SKILLS, P. 269
1. a) 2500 m
3 cm
2 cm
b) 7.5 cm
2. The prisms are not similar.
3. Colin is correct as there is enough information
sides are proportional.
sides are proportional and all the angles are
b) No, the rectangles will not be similar.
right angles.
3.
1.5 cm
to mat 1 or mat 2.
5. Consider two rectangles, one with sides ℓ and
w, and the other with sides double the length,
3 cm
a) Yes, the squares are similar because the
given to determine that corresponding
4. Mats 1 and 2 are similar. Mat 3 is not similar
2 cm
4 cm
1 cm
4. a) scale factor: approximately 0.0039
2ℓ and 2w. The area of the second rectangle is 4
times the area of the first; this is not the same
proportion as the sides.
b) 0.7 cm
5. a) 1.25 feet
b) 1:8