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.

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

   2.2

2. 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).

3. 2.

   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
4. 3.

   Kira draws a small triangle FQS inside a big triangle FGH. How many cm long is the leftover piece QG?

   3
5. 4.

   Milo draws a small triangle SUV inside a big triangle SYW. How many cm long is the leftover piece UY?

   21
6. 5.

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

   22

7. Use this

   The bulb is straight above the lamp's base. The shadow's tip is 15 cm beyond the toy along the table. The bulb, the top of the toy and the tip of the shadow lie on one straight line (sketch, not to scale).

8. 6.

   Ren stands a 10 cm toy on a table, 45 cm from the base of a desk lamp. The toy's shadow is 15 cm long. How many cm above the table is the bulb?

   40

9. Use this

   The bulb, the top of the toy and the tip of the shadow lie on one straight line (sketch, not to scale).

10. 7.

    Zee stands a 6 cm toy on a table, 16 cm from the base of a desk lamp. The toy's shadow is 4 cm long. How many cm above the table is the bulb?

    30
11. 8.

    (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. 9.

    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 have a right angle at the ground, and light meets the mirror at equal angles, so two angles match
    • Both stand on the ground, and both are the same distance from the mirror, so the two triangles match

13. Use this

    Two players and the floor; the ball's path drawn as two slanted lines meeting at the bounce (sketch, not to scale).

14. 10.

    Esme bounce-passes a basketball to a partner. Why are the passer's triangle and the partner's triangle similar?

    • Both players stand on the floor, and both hold the ball at the same height, so the two triangles match
    • Both have a right angle below the hands, and the ball meets the floor at equal angles, so two angles match
    • Both touch the floor, and the ball meets it at equal angles, so one angle matches and that is enough