Proving the Angle-Angle-Side Theorem

[pholee95]

Hello everyone. I need help on proofs. I have to proof the Angle-Angle-Side theorem. Can someone help me with this?

The AAS states : If triangles ABC and DEF are two triangles such that angle ABC is congruent to angle DEF, angle BCA is congruent to angle EFD, and segment AC is congruent to DF, then triangles ABC and DEF are congruent.

Thank You!

 

[soroban]

Hello everyone. i have to proof the Angle-Angle-Side theorem.
Can someone help me with this?

The AAS states : If triangles ABC and DEF are two triangles such that angle ABC is congruent to angle DEF,
angle BCA is congruent to angle EFD, and segment AC is congruent to DF,
then triangles ABC and DEF are congruent.

Since two pairs of angles are congruent, the third pair is also congruent.
. . That is: $$\angle BAC = \angle EDF.$$

We have: $$\angle ACB = \angle DFE.\;AC = DF,\;\angle BAC = \angle EDF.$$

The triangles are congruent by ASA.

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