Worksheet

Similar figures: corresponding sides, scale factor, and all circles are similar

Grade 10 Math Worksheet - Challenge Me

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Circle the best answer.

  1. Ari says △DEF is a scaled copy of △ABC. Which moves carry △ABC onto △DEF, and what do they show?

    • Dilate by 4 about A, then slide 2 right and 1 up: similar, with ratio 4
    • Dilate by 2 about A, then slide 2 right and 1 up: congruent, with equal sides
    • Slide 2 right and 1 up, then dilate by 2 about A: similar, with ratio 2
    • Dilate by 2 about A, then slide 2 right and 1 up: similar, with ratio 2

  2. Esme wants one dilation that carries △ABC onto △DEF. Is that possible?

    • No: AB to DE is 2 but AC to DF is 3, so no single factor fits
    • Yes: dilate by 2.5, the average of 2 and 3
    • Yes: dilate by 2 about A, because both are right triangles with a shared corner
    • Yes: dilate by 3 about A, since AC to DF is a ratio of 3

  3. Jun applies a dilation and then rigid motions to a triangle. Which statement is true for every such similarity transformation?

    • Perimeters are kept and angles are not, since a dilation bends the sides
    • Side lengths are kept, as in a rigid motion, so the image is congruent
    • Areas are kept, because the shape is the same and just the position changes
    • Angle measures and ratios of sides are kept; lengths and areas are not

  4. The sun makes the same angle with the ground for both. Both objects stand straight up. Kira stands a 1.5 m stick in the sun. Its shadow is 2 m. A tree's shadow is 14 m at the same time. Which setup finds the tree's height h?

    • Same angles give AA, but 1.5/2 = 14/h
    • Shadows add to the height, so h = 14 − 2 + 1.5
    • Same sun angle and a right angle each give AA, so 1.5/2 = h/14
    • Both are shadows, so the triangles are similar and 1.5/14 = 2/h

  5. Luz's eyes are 1.6 m high, 2.4 m from a mirror on the ground. The tree's base is 9 m from the mirror. Luz sees the treetop. Which setup finds the height h?

    • Equal angles at the mirror and two right angles give AA, so 1.6/2.4 = h/9
    • Equal angles give AA, but 1.6/2.4 = h/(9 + 2.4), using the whole ground distance
    • The triangles are similar, and 1.6/9 = h/2.4, putting each height over the other distance
    • Heights differ by the distances, so h = 1.6 + 9 − 2.4

  6. Milo is 1.6 m tall and stands under a 4.8 m lamp post. Milo's shadow is 2 m. Which setup finds the distance d from the post's base to Milo?

    • They share an angle, but 4.8/(d + 2) = 2/1.6, with the sides in the other order
    • The two right triangles share an angle (AA), so 4.8/(d + 2) = 1.6/2
    • They share an angle, but 4.8/d = 1.6/2, taking the large base as d
    • The heights differ by 3.2, so d + 2 = 4.8 − 1.6 and the distance is 1.2 m

  7. similar, with scale factor 3 from the first to the second. Pia enlarges a poster to 3 times its width and height. Ink follows area, and the frame follows the edge length. How do the costs change?

    • Ink costs 3 times as much; the frame costs 3 times as much
    • Ink costs 9 times as much; the frame costs 3 times as much
    • Ink costs 9 times as much; the frame costs 9 times as much
    • Ink costs 27 times as much; the frame costs 9 times as much

  8. Ren makes a cube planter 30 cm on each edge, then one 60 cm on each edge. Soil follows volume, paint follows surface area, and tape follows edge length. How do they change?

    • Soil 8 times, paint 4 times, tape 2 times
    • Soil 4 times, paint 4 times, tape 2 times
    • Soil 8 times, paint 8 times, tape 4 times
    • Soil 2 times, paint 2 times, tape 2 times

  9. similar and solid, same material. Tala builds a solid 1:10 model statue that weighs 3 kg. The real statue is solid and made of the same stone. What does it weigh?

    • 300 kg, because the surface grows 100 times and the weight follows it
    • 30 kg, because each measurement grows 10 times and so does the weight
    • 3000 kg, because weight follows volume: 3 × 10 × 10 × 10
    • 9 kg, because the 3 kg model is multiplied by 3 for each of the three dimensions

  10. Zee's 2-cup cake recipe fills a pan. Zee wants a pan with double the length, width and height. How much batter should Zee make?

    • 8 cups, because volume grows by 2 × 2 = 4 for a flat pan
    • 4 cups, because volume grows by 2
    • 16 cups, because volume grows by 2 × 2 × 2 = 8
    • 6 cups, because 3 more dimensions add 4 cups
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Similar figures: corresponding sides, scale factor, and all circles are similar

Answer Key - Grade 10 Math Worksheet - Challenge Me

Circle the best answer.

  1. Ari says △DEF is a scaled copy of △ABC. Which moves carry △ABC onto △DEF, and what do they show?

    • Dilate by 4 about A, then slide 2 right and 1 up: similar, with ratio 4
    • Dilate by 2 about A, then slide 2 right and 1 up: congruent, with equal sides
    • Slide 2 right and 1 up, then dilate by 2 about A: similar, with ratio 2
    • Dilate by 2 about A, then slide 2 right and 1 up: similar, with ratio 2

  2. Esme wants one dilation that carries △ABC onto △DEF. Is that possible?

    • No: AB to DE is 2 but AC to DF is 3, so no single factor fits
    • Yes: dilate by 2.5, the average of 2 and 3
    • Yes: dilate by 2 about A, because both are right triangles with a shared corner
    • Yes: dilate by 3 about A, since AC to DF is a ratio of 3

  3. Jun applies a dilation and then rigid motions to a triangle. Which statement is true for every such similarity transformation?

    • Perimeters are kept and angles are not, since a dilation bends the sides
    • Side lengths are kept, as in a rigid motion, so the image is congruent
    • Areas are kept, because the shape is the same and just the position changes
    • Angle measures and ratios of sides are kept; lengths and areas are not

  4. The sun makes the same angle with the ground for both. Both objects stand straight up. Kira stands a 1.5 m stick in the sun. Its shadow is 2 m. A tree's shadow is 14 m at the same time. Which setup finds the tree's height h?

    • Same angles give AA, but 1.5/2 = 14/h
    • Shadows add to the height, so h = 14 − 2 + 1.5
    • Same sun angle and a right angle each give AA, so 1.5/2 = h/14
    • Both are shadows, so the triangles are similar and 1.5/14 = 2/h

  5. Luz's eyes are 1.6 m high, 2.4 m from a mirror on the ground. The tree's base is 9 m from the mirror. Luz sees the treetop. Which setup finds the height h?

    • Equal angles at the mirror and two right angles give AA, so 1.6/2.4 = h/9
    • Equal angles give AA, but 1.6/2.4 = h/(9 + 2.4), using the whole ground distance
    • The triangles are similar, and 1.6/9 = h/2.4, putting each height over the other distance
    • Heights differ by the distances, so h = 1.6 + 9 − 2.4

  6. Milo is 1.6 m tall and stands under a 4.8 m lamp post. Milo's shadow is 2 m. Which setup finds the distance d from the post's base to Milo?

    • They share an angle, but 4.8/(d + 2) = 2/1.6, with the sides in the other order
    • The two right triangles share an angle (AA), so 4.8/(d + 2) = 1.6/2
    • They share an angle, but 4.8/d = 1.6/2, taking the large base as d
    • The heights differ by 3.2, so d + 2 = 4.8 − 1.6 and the distance is 1.2 m

  7. similar, with scale factor 3 from the first to the second. Pia enlarges a poster to 3 times its width and height. Ink follows area, and the frame follows the edge length. How do the costs change?

    • Ink costs 3 times as much; the frame costs 3 times as much
    • Ink costs 9 times as much; the frame costs 3 times as much
    • Ink costs 9 times as much; the frame costs 9 times as much
    • Ink costs 27 times as much; the frame costs 9 times as much

  8. Ren makes a cube planter 30 cm on each edge, then one 60 cm on each edge. Soil follows volume, paint follows surface area, and tape follows edge length. How do they change?

    • Soil 8 times, paint 4 times, tape 2 times
    • Soil 4 times, paint 4 times, tape 2 times
    • Soil 8 times, paint 8 times, tape 4 times
    • Soil 2 times, paint 2 times, tape 2 times

  9. similar and solid, same material. Tala builds a solid 1:10 model statue that weighs 3 kg. The real statue is solid and made of the same stone. What does it weigh?

    • 300 kg, because the surface grows 100 times and the weight follows it
    • 30 kg, because each measurement grows 10 times and so does the weight
    • 3000 kg, because weight follows volume: 3 × 10 × 10 × 10
    • 9 kg, because the 3 kg model is multiplied by 3 for each of the three dimensions

  10. Zee's 2-cup cake recipe fills a pan. Zee wants a pan with double the length, width and height. How much batter should Zee make?

    • 8 cups, because volume grows by 2 × 2 = 4 for a flat pan
    • 4 cups, because volume grows by 2
    • 16 cups, because volume grows by 2 × 2 × 2 = 8
    • 6 cups, because 3 more dimensions add 4 cups