Skills · Geometry · Similarity

Similar triangles

Printable practice with an answer key the engine computes, at three levels, in as many versions as you need.

Problem types

Sample Sheet · Level 1

  1. triangle ABC, D on AB and E on AC, DE parallel to BC: AD 12, DB 15, AE 16, EC ?ABCDE121516?
    Find the length marked ?.
  2. triangles ABC and DEF, ∠B and ∠E marked equal, ∠C and ∠D marked equal: AB 18, BC 30, AC 27, DE ?, DF 9ABCDEF183027?9
    Find the length marked ?.
  3. triangle ABC, D on AB and E on AC, DE parallel to BC: AD 6, DB 2, DE 6, BC ?ABCDE626?
    Find the length marked ?.
  4. triangles ABC and DEF, ∠A and ∠D marked equal, ∠B and ∠F marked equal: AB 9, BC 10, AC 12, EF 20, DF ?ABCDEF9101220?
    Find the length marked ?.
  5. triangles ABC and DEF, ∠B and ∠D marked equal, ∠C and ∠F marked equal: AB 11, BC 13, AC 14, DE 22, DF ?ABCDEF11131422?
    Find the length marked ?.
  6. triangle ABC, D on AB and E on AC, DE parallel to BC: AD 12, DB 4, AE 15, EC ?ABCDE12415?
    Find the length marked ?.
  7. triangle ABC, D on AB and E on AC, DE parallel to BC: AD 15, DB 6, DE 20, BC ?ABCDE15620?
    Find the length marked ?.
  8. triangle ABC, D on AB and E on AC, DE parallel to BC: AD 8, DB 4, DE 8, BC ?ABCDE848?
    Find the length marked ?.

Answer key

  1. 20 units
  2. 10 units
  3. 8 units
  4. 18 units
  5. 26 units
  6. 5 units
  7. 28 units
  8. 12 units

Sample Sheet · Level 3

  1. A 6-foot person casts a 7-foot shadow. At the same time, a tree casts a 35-foot shadow. How tall is the tree?
  2. triangle ABC, D on AB and E on AC, DE parallel to BC: AD 16, DB 12, AE (4x − 8), EC (x + 4)ABCDE1612(4x − 8)(x + 4)
    Find AE.
  3. triangle ABC, D on AB and E on AC, DE parallel to BC: AD 10, DB 4, DE (4x − 13), BC (x + 14)ABCDE104(4x − 13)(x + 14)
    Find BC.
  4. triangle ABC, D on AB and E on AC, DE parallel to BC: AD 12, DB 15, AE (4x − 20), EC (x + 3)ABCDE1215(4x − 20)(x + 3)
    Find EC.
  5. triangles ABC and DEF, ∠B and ∠E marked equal, ∠C and ∠D marked equal: AB 20, BC (3x − 2), AC 12, DE (x + 2), DF 6ABCDEF20(3x − 2)12(x + 2)6
    Find DE.
  6. triangle ABC, D on AB and E on AC, DE parallel to BC: AD 4, DB 2, DE (4x − 8), BC (x + 3)ABCDE42(4x − 8)(x + 3)
    Find BC.
  7. triangles ABC and DEF, ∠A and ∠E marked equal, ∠C and ∠F marked equal: AB 24, BC 15, AC (2x + 3), DE 16, EF (2x − 4)ABCDEF2415(2x + 3)16(2x − 4)
    Find EF.
  8. triangle ABC, D on AB and E on AC, DE parallel to BC: AD 8, DB 10, AE (x + 10), EC (3x + 9)ABCDE810(x + 10)(3x + 9)
    Find EC.

Answer key

  1. 30 feet
  2. 12 units
  3. 21 units
  4. 10 units
  5. 8 units
  6. 6 units
  7. 14 units
  8. 15 units

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