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Similar Triangles Worksheets

Identify similar and non-similar triangle pairs using SSS, SAS or AA, and write the matching vertex order with a worked answer key.

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Decide whether the triangles are similar. If they are, give a valid criterion and matching vertex statement.

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Use only the marked hypothesis

SSS needs three proportional side pairs. SAS needs the included angle between two proportional side pairs. AA needs two matching angles.

Learning objective

What this activity builds

Justify triangle similarity and name corresponding vertices in order.

Worked example

Two triangles have sides 3, 4, 5 and 6, 8, 10. Are they similar?

Yes, by SSS similarity.

Each corresponding side of the second triangle is twice the first: 6/3 = 8/4 = 10/5 = 2.

Teaching notes

Make the practice count

  • For SAS, the equal angle must be between the two compared sides.
  • For AA, two matching angles force the third to match.
  • Check the vertex order rather than copying the drawing orientation.

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Choose the similarity criteria and whether the set includes non-similar pairs.

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Math SheetNameScoreTeacherDateSimilar TrianglesDetermine whether each pair is similar, justify the result from the shown givens, and write the vertex correspondence when similar.1.Are the triangles similar? Justify from the shown givens. If yes, write a similarity statement in corresponding order.48 deg64 degABC48 deg64 degDEFSimilar?Justification and correspondence:2.Are the triangles similar? Justify from the shown givens. If yes, write a similarity statement in corresponding order.6810ABC121621DEFSimilar?Justification and correspondence:Diagrams are not to scale.math-sheet.comPage 1 of 4
Math SheetNameScoreTeacherDateSimilar TrianglesDetermine whether each pair is similar, justify the result from the shown givens, and write the vertex correspondence when similar.3.Are the triangles similar? Justify from the shown givens. If yes, write a similarity statement in corresponding order.2428AXB96112DCSimilar?Justification and correspondence:4.Are the triangles similar? Justify from the shown givens. If yes, write a similarity statement in corresponding order.1530ABC4591DEFSimilar?Justification and correspondence:Diagrams are not to scale.math-sheet.comPage 2 of 4
Math SheetNameScoreTeacherDateSimilar TrianglesDetermine whether each pair is similar, justify the result from the shown givens, and write the vertex correspondence when similar.5.Are the triangles similar? Justify from the shown givens. If yes, write a similarity statement in corresponding order.91215ABC273645DEFSimilar?Justification and correspondence:6.Are the triangles similar? Justify from the shown givens. If yes, write a similarity statement in corresponding order.40 deg55 degABC40 deg57 degEFSimilar?Justification and correspondence:Diagrams are not to scale.math-sheet.comPage 3 of 4
Math SheetNameScoreTeacherDateSimilar TrianglesDetermine whether each pair is similar, justify the result from the shown givens, and write the vertex correspondence when similar.7.Are the triangles similar? Justify from the shown givens. If yes, write a similarity statement in corresponding order.48 deg61 degABC48 deg61 degEFSimilar?Justification and correspondence:8.Are the triangles similar? Justify from the shown givens. If yes, write a similarity statement in corresponding order.91215ABC182431DEFSimilar?Justification and correspondence:Diagrams are not to scale.math-sheet.comPage 4 of 4

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