What can you conclude about BC in △ ABC and △ DBC?
See solution.
Practice makes perfect
If we can show that △ ABD ≅ △ CBD , then we can prove that ∠ A ≅ ∠ C. Since the two triangles share BD as a side, we can by the Reflexive Property of Congruence say that these sides are congruent. Let's mark this in our diagram.
Since the three sides of △ ABD are congruent to corresponding sides of △ CBD, we can by the SSS Congruence Theorem prove that △ ABD ≅ △ CBD. Now, we can also say that ∠ A ≅ ∠ C since these are corresponding angles.
