SSSS: Similar Quads?
- Tim Brzezinski
Recall that the SSS Triangle Similarity Theorem states that if all 3 sides of one triangle are in proportion to all 3 sides of another triangle, then those triangles are similar. (For an informal proof of this theorem, go to https://tube.geogebra.org/m/yKFwXvRj). Yet does the same hold true for quadrilaterals? That is, if all 4 sides of one quadrilateral are in proportion to all 4 sides of another quadrilateral, can we claim that those two quadrilaterals are similar? Since congruence of polygons is a special case of similarity of polygons (where the scale factor = 1), can we conclude that if 4 sides of one quadrilateral are congruent to 4 sides of another quadrilateral, then those quadrilaterals are congruent? (In essence, if the SSS Theorem proves triangles congruent, is there such an "SSSS Theorem" that proves 2 quadrilaterals congruent?) Interact with the applet below and respond to these questions.