Proving Triangle Congruence: Angle ABC & ABD

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Homework Help Overview

The discussion revolves around proving the congruence of triangles ACB and ADB, given that angle ABC is congruent to angle ABD and angle ACB is congruent to angle ADB. The subject area is geometry, specifically focusing on triangle congruence theorems.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the use of the angle-side-angle (ASA) theorem and discuss the relationships between angles in the triangles. Questions arise about how to apply theorems and the implications of angle congruences.

Discussion Status

Some participants have offered guidance on utilizing the ASA theorem and have engaged in reasoning about the relationships between the angles. There appears to be a productive exchange of ideas, with some participants expressing understanding of the concepts discussed.

Contextual Notes

Participants are navigating the constraints of the proof requirements and theorems applicable to triangle congruence without providing a complete solution.

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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!
 
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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.
 
yeah...i think i could use the ASA theorem...but i don't know how to explain it and when to use it.
 
You know that the sum of the interior angles of a triangle is always the same, right?
 
yes.
 
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
 
oh...i get it now! thanx!
 

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