Sample Proof on Triangle Congruence Part 3

Recall that for real numbers a, b, and c are real numbers, if $latex a = b$ and $latex b = c$, then $latex a = c$. This is called Transitive Property of Equality. This is also the same with congruence. If $latex A$, $latex B$, and $latex C$ are polygons, and if $latex A$ is congruent to $latex B$, and $latex B$ is congruent $latex C$, then $latex A$ is congruent to $latex C$. This is called the Transitive Property of Congruence. We will use this to prove the following problem.

Given: $latex \overline{BE} \cong \overline{DC}$ and $latex \overline{BD} \cong \overline{CA}$.

Prove: $latex \triangle DBE \cong \triangle CAB$.


It is given that $latex \overline{BE} \cong \overline{DC}$.

triangle congruence

Now, by reflexive property, that is a segment is congruent to itself, $latex \overline{BD} \cong \overline{BD}$.  Continue reading

Sample Proof on Triangle Congruence Part 1

We have discussed triangle congruence and in this series, we are going to use the congruence theorems in order to prove that two triangles are congruent.


$latex \overline{AB} \cong \overline{AE}$
$latex \overline{AC} \cong \overline{AD}$

$latex \overline{BD} \cong \overline{EC}$


We can see that there are two overlapping triangles: triangle $latex ADB$ and triangle $latex ACE$. Continue reading