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Similar Polygons Worksheets

Decide whether polygon pairs are similar and find scale factors, with triangles, rectangles, trapezoids, parallelograms and other quadrilaterals.

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Use the labelled measurements and correspondence, not the apparent drawing size.

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Keep the correspondence fixed

Compare side ratios in the printed vertex order. For general quadrilaterals, matching angles matter as well as proportional sides.

Learning objective

What this activity builds

Compare corresponding angles and side lengths to establish similarity.

Worked example

A rectangle is 4 by 6. A second rectangle is 6 by 9. Are they similar?

Yes. The smaller-to-larger scale factor is 3/2.

Both pairs of sides have the same ratio: 6/4 = 9/6 = 3/2. All corresponding angles are right angles.

Teaching notes

Make the practice count

  • Write ratios in the same direction.
  • For general polygons, check angles as well as sides.
  • A rotated or reflected copy can still be similar.

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Choose the polygon families. The preview and answer download use the same labelled correspondence.

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Math SheetNameScoreTeacherDateSimilar PolygonsUse the printed correspondence to decide similarity or find the smaller-to-larger scale factor. Check corresponding angles and side ratios.1.Are these polygons similar? Justify using the printed correspondence.34553.13 deg36.87 degABC9121553.13 deg36.87 degEFGCorrespondence: A<->E, B<->F, C<->GSimilar?2.Are these polygons similar? Justify using the printed correspondence.1610161070 deg110 deg70 deg110 degABCD2418241870 deg110 deg70 deg110 degEFGHCorrespondence: A<->E, B<->F, C<->G, D<->HSimilar?Diagrams are not to scale.math-sheet.comPage 1 of 4
Math SheetNameScoreTeacherDateSimilar PolygonsUse the printed correspondence to decide similarity or find the smaller-to-larger scale factor. Check corresponding angles and side ratios.3.Are these polygons similar? Justify using the printed correspondence.123sqrt(10)159108.43 deg71.57 degABCD72/5(18/5)sqrt(10)1854/5108.43 deg71.57 degEFGHCorrespondence: A<->E, B<->F, C<->G, D<->HSimilar?4.Are these polygons similar? Justify using the printed correspondence.24204020113.58 deg113.58 deg66.42 deg66.42 degABCD42358435126.87 deg126.87 deg53.13 deg53.13 degEFGHCorrespondence: A<->E, B<->F, C<->G, D<->HSimilar?Diagrams are not to scale.math-sheet.comPage 2 of 4
Math SheetNameScoreTeacherDateSimilar PolygonsUse the printed correspondence to decide similarity or find the smaller-to-larger scale factor. Check corresponding angles and side ratios.5.These polygons are similar. Find the scale factor from the smaller polygon to the larger polygon.8585ABCD32/320/332/320/3EFGHCorrespondence: A<->E, B<->F, C<->G, D<->HScale factor:6.These polygons are similar. Find the scale factor from the smaller polygon to the larger polygon.681053.13 deg36.87 degABC15202553.13 deg36.87 degEFGCorrespondence: A<->E, B<->F, C<->GScale factor:Diagrams are not to scale.math-sheet.comPage 3 of 4
Math SheetNameScoreTeacherDateSimilar PolygonsUse the printed correspondence to decide similarity or find the smaller-to-larger scale factor. Check corresponding angles and side ratios.7.These polygons are similar. Find the scale factor from the smaller polygon to the larger polygon.123sqrt(10)159108.43 deg71.57 degABCD246sqrt(10)3018108.43 deg71.57 degEFGHCorrespondence: A<->E, B<->F, C<->G, D<->HScale factor:8.These polygons are similar. Find the scale factor from the smaller polygon to the larger polygon.32203220ABCD160/3100/3160/3100/3EFGHCorrespondence: A<->E, B<->F, C<->G, D<->HScale factor:Diagrams are not to scale.math-sheet.comPage 4 of 4

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