illustration of why SSA may not prove congruence

SSA cannot be used to prove that two triangles are congruent when the angles that are known to be congruent are acute. Below is an illustration of how this can happen.

In the picture below, $\mathrm{△}ABC$ and $\mathrm{△}ABD$ share the angle $\mathrm{\angle }A$ and the side $\overline{AB}$, and the line segments $\overline{BC}$ and $\overline{BD}$ are congruent; however, $\mathrm{△}ABC$ and $\mathrm{△}ABD$ are clearly not congruent.

Title	illustration of why SSA may not prove congruence
Canonical name	IllustrationOfWhySSAMayNotProveCongruence
Date of creation	2013-03-22 17:04:11
Last modified on	2013-03-22 17:04:11
Owner	Wkbj79 (1863)
Last modified by	Wkbj79 (1863)
Numerical id	6
Author	Wkbj79 (1863)
Entry type	Example
Classification	msc 97D70
Classification	msc 51M99
Classification	msc 51-01