Missing sides of similar triangles, and shadow problems

Answer Key - Grade 8 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Ren lays a mirror flat on the ground and sees the top of a school in it. How many meters tall is the school?

   12.8
2. 2.

   Tala lays a mirror flat on the ground and sees the top of a house in it. How many meters tall is the house?

   9.6
3. 3.

   Ari bounce-passes a basketball to a partner 4 m away. How many meters from Ari does the ball hit the floor?

   2.2

4. Read this first

   Use this

   Esme's hands are 1.5 m high and the partner's hands are 1 m high. The ball hits the floor and leaves it at the same angle (sketch, not to scale).

5. 4.

   Esme bounce-passes a basketball to a partner 4.5 m away. How many meters from Esme does the ball hit the floor?

   2.7

6. Use this

   Jun's hands are 1.4 m high and the partner's hands are 0.6 m high. The ball hits the floor and leaves it at the same angle (sketch, not to scale).

7. 5.

   Jun bounce-passes a basketball to a partner 4 m away. How many meters from Jun does the ball hit the floor?

   2.8
8. 6.

   Luz draws a small triangle CDU inside a big triangle CVW. How many cm long is the leftover piece DV?

   7
9. 7.

   Noah draws a small triangle GQD inside a big triangle GHF. How many cm long is the leftover piece QH?

   22
10. 8.

    Tala stands a 15 cm toy on a table, 24 cm from the base of a desk lamp. The toy's shadow is 12 cm long. How many cm above the table is the bulb?

    45
11. 9.

    (sketch, not to scale). Ari measures a stick and a tree that both stand straight up and cast shadows at the same time. Why are the stick's triangle and the tree's triangle similar?

    • Both have a right angle at the ground, and the sun makes the same angle with the ground, so two angles match
    • Both cast shadows, and the sun makes the same angle with the ground, so one angle matches and that is enough
    • Both stand on the ground, and both are the same height, so the two triangles match
12. 10.

    Bo sees the top of a tower in a mirror on the ground. Why are Bo's triangle and the tower's triangle similar?

    • Both look into the mirror, and light meets it at equal angles, so one angle matches and that is enough
    • Both stand on the ground, and both are the same distance from the mirror, so the two triangles match
    • Both have a right angle at the ground, and light meets the mirror at equal angles, so two angles match