given: AB is congruent to CB , angle ABD is congruent to angle CBD prove: triangle ABD is congruent to triangle CBD

Question

what is the 2 column proof that i would write?

Answer 1

We will use the SAS (SIDE-ANGLE-SIDE) to prove that the two triangles are congruent.  This states that if two sides and the included angle in one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

 

First line

First column: AB is congruent to CB      Second column: Given

Second line

First column: angle ABD is congruent to angle CBD      Second column: Given

 

At this point we have the  SIDE-ANGLE portion of SAS.  We just need the other side.  We can see from the given angles that they both share a side...BD.

 

Third Line

First column: BD is congruent to BD     Second column: Reflexive property

 

All that is left is to state SAS.

 

Fourth Line

First Column:  Triangle ABD is congruent to triangle CBD     Second column: SAS (from lines 1,2,3)