Why can't you prove triangles congruent by using side-side-angle?

1 Answer
Jan 3, 2016

Side-side-angle congruence does not guarantee that the triangles are congruent: two triangles can be made from each side-side-angle set.

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See how in Figures 3-B and 3-D there are two triangles which have two congruent sides (AB and BC) and the congruent angle A, but neither triangle is congruent.

Two triangles can be made through the side-side-angle description (unless the angle is a right angle, which can be used to prove congruence, in the hypotenuse-leg theorem).