Skills · Geometry · Similarity

Similar polygons

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 ∼ triangle DEF: AB 13, BC 9, AC 11, EF 18ABCDEF1391118
    Find the scale factor from △ABC to △DEF.
  2. triangle ABC ∼ triangle DEF: AB 16, BC 24, AC 18, DE 8ABCDEF1624188
    Find the scale factor from △ABC to △DEF.
  3. triangle ABC ∼ triangle DEF: AB 20, BC 24, AC 28, DF 7ABCDEF2024287
    Find the scale factor from △ABC to △DEF.
  4. quadrilateral ABCD ∼ quadrilateral EFGH: AB 18, BC 24, CD 30, AD 6, EF 12ABCDEFGH182430612
    Find the scale factor from ABCD to EFGH.
  5. quadrilateral ABCD ∼ quadrilateral EFGH: AB 18, BC 10, CD 14, AD 16, FG ?, GH 21ABCDEFGH18101416?21
    ABCD ∼ EFGH. Find the length marked ?.
  6. triangle ABC ∼ triangle DEF: AB 10, BC 14, AC 16, DE 5, DF ?ABCDEF1014165?
    △ABC ∼ △DEF. Find the length marked ?.
  7. quadrilateral ABCD ∼ quadrilateral EFGH: AB 17, BC 10, CD 13, AD 6, FG 20, EH ?ABCDEFGH171013620?
    ABCD ∼ EFGH. Find the length marked ?.
  8. triangle ABC ∼ triangle DEF: AB 15, BC 18, AC 21, EF ?, DF 7ABCDEF151821?7
    △ABC ∼ △DEF. Find the length marked ?.

Answer key

  1. 2
  2. 12
  3. 14
  4. 23
  5. 15 units
  6. 8 units
  7. 12 units
  8. 6 units

Sample Sheet · Level 3

  1. triangle ABC ∼ triangle DEF: AB 12, BC 18, AC 14, EF 36ABCDEF12181436
    △ABC ∼ △DEF. Find the perimeter of △DEF.
  2. triangle ABC ∼ triangle DEF: AB 10, BC 7, AC 9, DF 27ABCDEF107927
    △ABC ∼ △DEF. Find the perimeter of △DEF.
  3. triangle ABC ∼ triangle DEF: AB 18, BC 24, AC 16, EF 12ABCDEF18241612
    Find the scale factor from △ABC to △DEF.
  4. triangle ABC ∼ triangle DEF: AB 21, DE 7ABCDEF217
    △ABC ∼ △DEF, and the area of △ABC is 117 square units. Find the area of △DEF.
  5. quadrilateral ABCD ∼ quadrilateral EFGH: AB 20, BC 28, CD 16, AD 24, FG 7ABCDEFGH202816247
    Find the scale factor from ABCD to EFGH.
  6. triangle ABC ∼ triangle DEF: AB 20, DE 15ABCDEF2015
    △ABC ∼ △DEF, and the area of △ABC is 208 square units. Find the area of △DEF.
  7. triangle ABC ∼ triangle DEF: AB 24, BC (3x + 6), AC 27, DE 16, EF (4x − 12)ABCDEF24(3x + 6)2716(4x − 12)
    △ABC ∼ △DEF. Find EF.
  8. quadrilateral ABCD ∼ quadrilateral EFGH: AB 6, BC 10, CD 14, AD (x + 15), EF 3, EH (3x − 5)ABCDEFGH61014(x + 15)3(3x − 5)
    ABCD ∼ EFGH. Find EH.

Answer key

  1. 88 units
  2. 78 units
  3. 12
  4. 13 square units
  5. 14
  6. 117 square units
  7. 20 units
  8. 10 units

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