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.

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

   22.5
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.

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

   25.6

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.

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

   21
10. 8.

    Pia stands a 12 cm toy on a table, 40 cm from the base of a desk lamp. The toy's shadow is 20 cm long. How many cm above the table is the bulb?

    36
11. 9.

    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
12. 10.

    Jun draws a small triangle FQS inside a big triangle FGH, sharing corner F, with QS parallel to GH. Why are the two triangles similar?

    • They share a corner, and one sits inside the other, so the two triangles match just by being nested together
    • They share the angle at corner F, and parallel lines make the other angles equal, so two angles match
    • They share a corner, and the angle at F is the same, so one angle matches and that is enough