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8th grade Missing sides of similar triangles, and shadow problems worksheet

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Missing sides of similar triangles, and shadow problems

Grade 8 Math Worksheet - Challenge Me

NameDate

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

  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?

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

  3. 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).

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

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

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

  7. 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?

  8. 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).

  9. 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?

  10. (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 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
    • Both have a right angle at the ground, and the sun makes the same angle with the ground, so two angles match

  11. 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

  12. 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 a corner, and the angle at F is the same, so one angle matches and that is enough
    • They share the angle at corner F, and parallel lines make the other angles equal, so two angles match
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8th grade Missing sides of similar triangles, and shadow problems worksheet – printable
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About this worksheet

Missing sides of similar triangles, and shadow problems. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can find a missing side or height from two similar triangles: shadows, a mirror on the ground, a bounce, a lamp, and a small triangle inside a big one.
  • I can pick the right sides to pair (the whole side of the big triangle, not the leftover piece) and set up a table with heights matched to heights and shadows to shadows.
  • I can say why the triangles are similar: two angles match.

Standard: 8.G.A.4 (partial), 8.EE.B.6 (partial)

Words to know

similar triangles: Same shape, maybe different size: matching angles equal, sides all grow by one number.

scale factor from small to big: How many times as long the big triangle's side is: big side ÷ small side.

shadow: The dark patch an object makes. Sun rays hit objects at the same angle at the same time.

the whole side: The full side of the big triangle, from the shared corner to the far corner.

the leftover piece: The part of that whole side that sticks out past the small triangle.

parallel: Two lines that never meet and stay the same distance apart.

bounce: A ball that hits the floor and leaves it at the same angle it came in.

Common mistakes

Used the scale factor the wrong way round: divided where the side or height needed multiplying.

Added a number where a scale factor multiplies: found the gap between two lengths and added it to the height. Try it together: if a 2 m stick has a 3 m shadow, how long is the shadow of a 4 m stick?

Put the numbers in the table the wrong way round: a shadow where a height belongs, or the reverse.

What to say

Ask: is the second triangle bigger or smaller, and should its side come out bigger or smaller?

Ask: which column is for heights and which is for shadows?

Questions parents ask

What is the most common mistake with missing sides of similar triangles, and shadow problems?

Used the scale factor the wrong way round: divided where the side or height needed multiplying.

How can I help my child with missing sides of similar triangles, and shadow problems?

Ask: is the second triangle bigger or smaller, and should its side come out bigger or smaller?

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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