Similar Triangles and Proving Similarity · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

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Mathematics · Geometry · ages 14-15
Name ______________________   Date ____________

  1. Two triangles have two pairs of equal angles. What follows?

    • The triangles are similar
    • The triangles are congruent
    • The triangles have the same area
    • Nothing follows

  2. Two triangles have two pairs of equal angles. What follows?

    • The triangles are similar
    • The triangles are congruent
    • The triangles have the same area

  3. Both triangles have angles of 50, 60 and 70 degrees. What follows?

    • They must be congruent
    • They must be similar
    • Nothing follows

  4. Amir matches the vertices first, then pairs shortest with shortest. Is Amir right?

    Circle one:   True   False

  5. Triangle A has sides 4, 6, 8. Similar triangle B has shortest side 10. What is the scale factor from A to B?

    • 2.5
    • 2
    • 4
    • 6

  6. Which pair of triangles must be similar?

    • Sides 3, 4, 5 against sides 4, 5, 6
    • Angles 50, 60, 70 in both triangles
    • Any two right triangles

  7. Two similar triangles have matching sides of 3 cm and 12 cm. A second side of the smaller is 5 cm. How long is its match in cm?

    Answer: ______________

  8. Two similar triangles have matching sides 3 cm and 12 cm. A second side of the smaller is 5 cm. How long is its match in cm?

    Answer: ______________

  9. Triangle A has sides 4, 6 and 8 cm. Similar triangle B has shortest side 10 cm. How long is the longest side of B in cm?

    Answer: ______________

  10. Ben writes a ratio from mismatched vertices and gets a wrong side, yet his triangles truly are similar. What went wrong?

    • Similarity was never proved
    • The pairing was wrong, so the scale factor was wrong
    • Similar triangles never share a scale factor
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Same shape, new size W1-mt_NPRVlr4lrs-s1

  1. The triangles are similar · Two matching angle pairs force the third to match, which is the AA test.
  2. The triangles are similar · Two matching pairs force the third to match, which is the test.
  3. They must be similar · All three angles match, so similarity is certain.
  4. True · Matching vertices before ratios is exactly the safe method.
  5. 2.5 · 10 divided by 4 is 2.5.
  6. Angles 50, 60, 70 in both triangles · Matching angles guarantee similarity; the other pairs can differ.
  7. 20 · The scale factor is 4, and 5 times 4 is 20.
  8. 20 · The scale factor is 12/3 = 4, and 5 × 4 = 20.
  9. 20 · The factor is 2.5, and 8 times 2.5 is 20.
  10. The pairing was wrong, so the scale factor was wrong · A ratio from wrong partners gives a wrong factor and a wrong side.
Worksheet · LightMySky