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?

   • 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 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
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 3 about A, since AC to DF is a ratio of 3
   • Yes: dilate by 2 about A, because both are right triangles with a shared corner
   • Yes: dilate by 2.5, the average of 2 and 3
3. 3.

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

   • Side lengths are kept, as in a rigid motion, so the image is congruent
   • 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
   • 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 sun angle and a right angle each give AA, so 1.5/2 = h/14
   • Same angles give AA, but 1.5/2 = 14/h
   • Shadows add to the height, so h = 14 − 2 + 1.5
   • Both are shadows, so the triangles are similar and 1.5/14 = 2/h
5. 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?

   • Heights differ by the distances, so h = 1.6 + 9 − 2.4
   • Equal angles at the mirror and two right angles give AA, so 1.6/2.4 = h/9
   • The triangles are similar, and 1.6/9 = h/2.4, putting each height over the other distance
   • Equal angles give AA, but 1.6/2.4 = h/(9 + 2.4), using the whole ground distance
6. 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 = 1.6/2, taking the large base as d
   • The two right triangles share an angle (AA), so 4.8/(d + 2) = 1.6/2
   • The heights differ by 3.2, so d + 2 = 4.8 − 1.6 and the distance is 1.2 m
   • They share an angle, but 4.8/(d + 2) = 2/1.6, with the sides in the other order
7. 7.

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

   • 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
   • 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?

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