Proving Triangle Congruence: Angle ABC & ABD

[hecate]

can anyone explain how to do this proof?
Given: angle ABC is congruent to angle ABD, angle ACB is congruent to angle ADB
Prove: triangle ACB is congruent to triangle ADB.
thank you!

 

[NateTG]

Do you have any theorems that you can use? Like the angle-side-angle theorem?

If you have that, and you can show that BAD and BAC are the same, then you're done.

 

[hecate]

yeah...i think i could use the ASA theorem...but i don't know how to explain it and when to use it.

 

[NateTG]

You know that the sum of the interior angles of a triangle is always the same, right?

 

[hecate]

yes.

 

[NateTG]

So you know that:
ABC + BCA + CAB = ABD + BDA + DAC

from the problem you have:
ABC=ABD
and
BCA=BDA

so if you make the substitutions you get
ABC+BCA+CAB=ABC+BCA+DAC

ABD+BCA can be cancellet from both sides, so you get
CAB=DAC

 

[hecate]

oh...i get it now! thanx!