Geometric Proofs Math Example 1

Solution

1. 1
   Given: Triangle $ABC$ with $AB = AC$. Draw the median from $A$ to the midpoint $M$ of $BC$.
2. 2
   In triangles $ABM$ and $ACM$: $AB = AC$ (given), $AM = AM$ (common side), $BM = CM$ ($M$ is the midpoint).
3. 3
   By SSS congruence, $\triangle ABM \cong \triangle ACM$.
4. 4
   Therefore $\angle ABC = \angle ACB$ as corresponding parts of congruent triangles.