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How do you prove this isosceles triangle?

Given $ AC$ = $BC$

Prove: $m\angle A=m\angle B$

I've gotten to the angle bisector and SAS(side- angle- side), and I believe there is one more step after that. I don't know what it is.

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1 Answer

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Short answer: Once you have proven the two triangles congruent via SAS (or however you did it), you only need to select corresponding angles of the congruent triangles; those will be identical in measure.

Incidentally, the classic proof requires the construction of the angle bisector. Here's one way to do it without any additional lines:

• $AC = BC$ (given)
• $BC = AC$ (symmetry)
• $BC = CB$ (identity)
• $\triangle CAB \cong \triangle CBA$ (SSS)
• $m\angle CAB = m\angle CBA$ (corresponding angles of congruent triangles)

Attributed to Pappas, I believe.

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