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1 Name: Class: Date: ID: A Ch. 6 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A doorway of width 3.25 ft and height 7.25 ft is similar to another doorway of width x and height 9.06 ft. What is the measure of x? a ft c ft b ft d ft 2. What is necessary to make the two shapes below similar? a. Their corresponding sides must be proportional and their corresponding areas also must be proportional. b. Their corresponding angles must be the same and their corresponding sides must be proportional. c. Their corresponding angles must be the same and their corresponding areas must be proportional. d. Their corresponding angles must be supplementary and their corresponding sides must be proportional. 3. If the scale on a map of the world is 750 km:1 cm, what distance would be represented by 12 cm on the map? a km c km b km d km 4. A drawing of a staircase measures 6 cm in height, but the actual staircase measures 660 cm in height. What is the scale factor? a. 110 c. 120 b. 105 d. 85 1
2 Name: ID: A 5. A right triangle has a base of 46 cm. A similar triangle has a base of 874 cm. How many times larger is the similar triangle? a. 19 c. 18 b. 17 d. 20 Short Answer 1. On the blueprint for a kitchen floor, the room measures 12 inches long and 10 inches wide. If the scale of the drawing is 1 inch:1.5 ft, what are the dimensions of the actual kitchen floor? 2. Are the triangles below similar? Explain. 3. In the diagram below, 1 cm:9.3 m. What is the length of side a in metres? (The figure is not drawn to scale.) 2
3 Name: ID: A 4. Janine constructed a dollhouse modelled after her own house. The hallway of the dollhouse is 6 inches long and 4 inches wide. If the hallway in her actual house is 9 feet long and 5 feet wide, is the dollhouse actually similar to Janine s house? 5. The diagrams below have the following dimensions: w = 22.1 mm a = 3.3 mm x = mm b = 6.1 mm y = mm c = 3 mm z = 9.75 mm d = 6.8 mm Are the two objects similar shapes? Explain. 6. What would be the length of a if the diagram below were scaled by a factor of 1.7? 7. A triangle has two interior angles of 37 and 82. A second triangle has two interior angles of 37 and 61. Are these two triangles similar? Explain.. 8. A triangle has side lengths of 32.7 mm, 47.7 mm, and 65.4 mm. The longest side of a similar triangle is mm. What are the lengths of its other two sides? 3
4 Name: ID: A 9. Gina drew a scale representation of a field (see Polygon C). For instance, she drew a line 2.2 cm to represent the actual measure (20 m) of this side (AD). Gina needs to complete the drawing of Polygon D so that both polygons are similar. Problem 1. Determine the value of the variable, rounded to 1 decimal place. a) 4 18 = w 104 b) = 128 x. 4
5 Name: ID: A 2. The diagrams below have the following dimensions: w = 7.8 a = 26 x = 7.5 b = 25 y = 3.9 c = 13 z = 8.4 d = 28 If the smaller figure was created as a reduction of the larger figure, what scale factor was used? 3. Calculate the value of side length x in the diagram if: a = 6 cm b = 9 cm c = 8 cm 4. In the picture below, a man observes his shadow on the ground. The casting of his shadow creates a similar triangle to that of the nearby building. If a is 2.4 m and b is 14.4 m, how tall is the building if the man is 1.6 m tall? 5
6 Ch. 6 Practice Test Answer Section MULTIPLE CHOICE 1. ANS: A PTS: 1 DIF: Moderate REF: 6.1 OBJ: Geometry LOC: G-SO3 TOP: Similar Polygons KEY: Similar Polygons 2. ANS: B PTS: 1 DIF: Difficult REF: 6.1 OBJ: Geometry LOC: G-SO3 TOP: Similar Polygons KEY: Similar Polygons 3. ANS: A PTS: 1 DIF: Easy REF: 6.2 OBJ: Geometry LOC: G-SO3 TOP: Determining if Two Polygons are Similar KEY: Scale 4. ANS: A PTS: 1 DIF: Easy REF: 6.3 OBJ: Geometry LOC: G-SO3 TOP: Drawing Similar Polygons KEY: Scale 5. ANS: A PTS: 1 DIF: Moderate REF: 6.4 OBJ: Geometry LOC: G-SO3 TOP: Similar Triangles KEY: Similar Triangles SHORT ANSWER 1. ANS: The scale of the blueprint is 1 inch:1.5 ft. To calculate the dimensions of the room, multiply each measurement on the blueprint by 1.5 and change the units from inches to feet. Length: Width: = 18 ft = 15 ft The kitchen is 18 ft by 15 ft. PTS: 1 DIF: Easy REF: 6.1 OBJ: Geometry LOC: G-SO3 TOP: Similar Polygons KEY: Similar Polygons 1
7 2. ANS: No, the triangles are not similar. This can be determined by comparing the corresponding angles of the two triangles. Both triangles are right triangles, but their other two angles are not corresponding. Calculate the other angle of the bottom triangle = None of the angles of the bottom triangle are equal to the angles of the top triangle; therefore, the triangles are not similar. PTS: 1 DIF: Moderate REF: 6.1 OBJ: Geometry LOC: G-SO3 TOP: Similar Polygons KEY: Similar Polygons 3. ANS: Side a is equal in length to the side opposite it. 1 cm equals 9.3 m, so multiply the length of the opposite side on the diagram by cm 9.3 m/cm 87.4 m The length of d is 87.4 m. PTS: 1 DIF: Difficult REF: 6.1 OBJ: Geometry LOC: G-SO3 TOP: Similar Polygons KEY: Similar Polygons 4. ANS: For the dollhouse and house to be similar, their dimensions must be proportional. Length: 9 6 = 1.5 Width: 5 4 = The scale factors of the dimensions of the hallway are not the same, so the dollhouse is not similar to the actual house. PTS: 1 DIF: Easy REF: 6.2 OBJ: Geometry LOC: G-SO3 TOP: Determining if Two Polygons are Similar KEY: Scale 2
8 5. ANS: Match up the corresponding sides by rotating the second object by 180. Calculate whether the ratios between the side lengths of the two shapes are equal. w d = w d = 3.25 x a = x a = 3.25 y b = y b = 3.25 z c = z c = 3.25 The ratios are the same, so the shapes are similar. PTS: 1 DIF: Easy REF: 6.2 OBJ: Geometry LOC: G-SO3 TOP: Determining if Two Polygons are Similar KEY: Scale 6. ANS: = 25.5 m The length of a would be 25.5 m. PTS: 1 DIF: Easy REF: 6.3 OBJ: Geometry LOC: G-SO3 TOP: Drawing Similar Polygons KEY: Scale 7. ANS: Yes. The first triangle has interior angles of 37, 82, and 61, because the sum of the angles in any triangle is 180. The second triangle has the same interior angles using the same rule. PTS: 1 DIF: Easy REF: 6.4 OBJ: Geometry LOC: G-SO3 TOP: Similar Triangles KEY: Similar Triangles 8. ANS: Calculate the scale factor between the longest sides of the two triangles = 11 The larger triangle is 11 times bigger than the smaller triangle. Calculate the lengths of the other two sides = mm = mm The other two sides of the larger triangle are mm and mm. PTS: 1 DIF: Moderate REF: 6.4 OBJ: Geometry LOC: G-SO3 TOP: Similar Triangles KEY: Similar Triangles 3
9 9. ANS: PTS: 1 PROBLEM 1. ANS: a) 4 18 = w = w = w 23.1 = w b) = 128 x x = 128 x 37 x 414x = x = x = PTS: 1 DIF: Easy REF: 6.2 OBJ: Geometry LOC: G-SO3 TOP: Determining if Two Polygons are Similar KEY: Proportional reasoning 4
10 2. ANS: Calculate the ratio between the side lengths = = = = 0.3 Each set of corresponding sides are related by a factor of 0.3. The scale factor is 0.3. PTS: 1 DIF: Easy REF: 6.3 OBJ: Geometry LOC: G-SO3 TOP: Drawing Similar Polygons KEY: Scale 3. ANS: ΔABC and ΔADE are similar because they share A, and right triangles are similar if one pair of corresponding angles is congruent. Calculate the ratio of side lengths. b a = 9 6 b a = 1.5 Therefore, the ratio between AB and AD must be 1.5. AD AB = 1.5 c + x c = 1.5 c + x = c 1.5 x = (c 1.5) c x = (8 1.5) 8 x = 12 8 x = 4 cm Side length x is 4 cm long. PTS: 1 DIF: Moderate REF: 6.4 OBJ: Geometry LOC: G-SO3 TOP: Similar Triangles KEY: Similar Triangles 5
11 4. ANS: Since the triangles are similar, a must be proportional to b, and x and y must be in the same proportion. b a = y x = y = y = y 9.6 = y The building is 9.6 m tall. PTS: 1 DIF: Difficult REF: 6.4 OBJ: Geometry LOC: G-SO3 TOP: Similar Triangles KEY: Similar Triangles 6
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