Draw two polygons that have corresponding angles that are all congruent but are not similar to prove that angle congruence is not enough to establish that two polygons are similar.

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Mathematics

Dean Hall

3 December, 09:52

Draw two polygons that have corresponding angles that are all congruent but are not similar to prove that angle congruence is not enough to establish that two polygons are similar.

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Raul Shepard · Answer 1

There are infinitely many ways to do this. One such way is to draw a very thin stretched out rectangle (say one that is very tall) and a square. Example: the rectangle is 100 by 2, while the square is 4 by 4.

Both the rectangle and the square have the same corresponding angle measures. All angles are 90 degrees.

However, the figures are not similar. You cannot scale the rectangle to have it line up with the square. The proportions of the sides do not lead to the same ratio

100/4 = 25

2/4 = 0.5

so 100/4 = 2/4 is not a true equation. This numerically proves the figures are not similar.

side note: if you are working with triangles, then all you need are two pairs of congruent corresponding angles. If you have more than three sides for the polygon, then you'll need to confirm the sides are in proportion along with the angles being congruent as well.