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

Grade 10 Math Worksheet - Challenge Me

Circle the best answer.

1. 1.

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

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

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

   • 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
   • No: AB to DE is 2 but AC to DF is 3, so no single factor fits
3. 3.

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

   • Angle measures and ratios of sides are kept; lengths and areas are not
   • 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
4. 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
   • Both are shadows, so the triangles are similar and 1.5/14 = 2/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
5. 5.

   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?

   • The heights differ by 3.2, so d + 2 = 4.8 − 1.6 and the distance is 1.2 m
   • The two right triangles share an angle (AA), so 4.8/(d + 2) = 1.6/2
   • They share an angle, but 4.8/(d + 2) = 2/1.6, with the sides in the other order
   • They share an angle, but 4.8/d = 1.6/2, taking the large base as d
6. 6.

   The plan wrote 2/3 = h/30. Noah measured a 2 m pole's shadow, 3 m, at noon. A building's shadow was 30 m at 5 pm. Noah says the building is 20 m tall. What is wrong?

   • The ratio should be 3/2 = h/30, with the shadow written over the height
   • The pole is shorter than the building, so it cannot be used
   • The shadows should be added to the heights first
   • The sun angle was different, so the two right triangles are not similar
7. 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 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
   • Ink costs 3 times as much; the frame costs 3 times as much
8. 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 4 times, paint 4 times, tape 2 times
   • Soil 8 times, paint 4 times, tape 2 times
   • Soil 2 times, paint 2 times, tape 2 times
   • Soil 8 times, paint 8 times, tape 4 times
9. 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?

   • 9 kg, because the 3 kg model is multiplied by 3 for each of the three dimensions
   • 3000 kg, because weight follows volume: 3 × 10 × 10 × 10
   • 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
10. 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?

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