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Using Similar Polygons Worksheets

Find missing corresponding sides in similar polygons using given scale ratios or known side pairs, with eight problems and worked answers.

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Each pair is given to be similar. Find the missing side or x.

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Read the ratio direction before multiplying

A left:right ratio of a:b means each right length is b/a times its corresponding left length. When no ratio is stated, form it from a fully known side pair.

Learning objective

What this activity builds

Use one scale factor to calculate an unknown corresponding length.

Worked example

The left:right scale ratio is 3:5. A left side is 12. What is the corresponding right side?

20.

The multiplier from left to right is 5/3, so 12 × 5/3 = 20.

Teaching notes

Make the practice count

  • Mark which figure contains the unknown.
  • If the scale ratio is not printed, use a fully known side pair.
  • Check that every corresponding pair uses the same multiplier.

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Math SheetNameScoreTeacherDateUsing Similar PolygonsUse corresponding sides in the printed left-to-right direction to find x.1.The polygons are similar with the printed correspondence. Find x. The left:right ratio is 2:5.1610161070 deg110 deg70 deg110 degABCDx252570 deg110 deg70 deg110 degEFGHCorrespondence: A<->E, B<->F, C<->G, D<->HLeft : right = 2:52.The polygons are similar with the printed correspondence. Find x. Infer the left:right ratio from a known corresponding pair.12x159108.43 deg71.57 degABCD72/5(18/5)sqrt(10)1854/5108.43 deg71.57 degEFGHCorrespondence: A<->E, B<->F, C<->G, D<->HDiagrams are not to scale.math-sheet.comPage 1 of 4
Math SheetNameScoreTeacherDateUsing Similar PolygonsUse corresponding sides in the printed left-to-right direction to find x.3.The polygons are similar with the printed correspondence. Find x. The left:right ratio is 3:5.32203220ABCD160/3160/3xEFGHCorrespondence: A<->E, B<->F, C<->G, D<->HLeft : right = 3:54.The polygons are similar with the printed correspondence. Find x. Infer the left:right ratio from a known corresponding pair.x5105113.58 deg113.58 deg66.42 deg66.42 degABCD18153015113.58 deg113.58 deg66.42 deg66.42 degEFGHCorrespondence: A<->E, B<->F, C<->G, D<->HDiagrams are not to scale.math-sheet.comPage 2 of 4
Math SheetNameScoreTeacherDateUsing Similar PolygonsUse corresponding sides in the printed left-to-right direction to find x.5.The polygons are similar with the printed correspondence. Find x. The left:right ratio is 1:2.681053.13 deg36.87 degABCx162053.13 deg36.87 degEFGCorrespondence: A<->E, B<->F, C<->GLeft : right = 1:26.The polygons are similar with the printed correspondence. Find x. Infer the left:right ratio from a known corresponding pair.2424xABCD32203220EFGHCorrespondence: A<->E, B<->F, C<->G, D<->HDiagrams are not to scale.math-sheet.comPage 3 of 4
Math SheetNameScoreTeacherDateUsing Similar PolygonsUse corresponding sides in the printed left-to-right direction to find x.7.The polygons are similar with the printed correspondence. Find x. The left:right ratio is 4:7.12162053.13 deg36.87 degABCx283553.13 deg36.87 degEFGCorrespondence: A<->E, B<->F, C<->GLeft : right = 4:78.The polygons are similar with the printed correspondence. Find x. Infer the left:right ratio from a known corresponding pair.65x5113.58 deg113.58 deg66.42 deg66.42 degABCD915/21515/2113.58 deg113.58 deg66.42 deg66.42 degEFGHCorrespondence: A<->E, B<->F, C<->G, D<->HDiagrams are not to scale.math-sheet.comPage 4 of 4

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