Triangles ABC and DBC have side BC common, AB = BD and AC = CD. A… - Vidyadip

Question

Triangles ABC and DBC have side BC common, AB = BD and AC = CD. Are the two triangles congruent? State in symbolic form, which congruence do you use? Does $\angle\text{ABD}$ equal $\angle\text{ACD}?$ Why or why not?

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Answer

Yes,
Given,
$\triangle\text{ABC}$ and $\triangle\text{DBC}$ have side BC common, AB = BD and AC = CD
By SSS criterion of congruency, $\triangle\text{ABC}\cong\triangle\text{DBC}$
No, $\angle\text{ABD}$ and $\angle\text{ACD}$ are not equal because $\text{AB}\ne\text{AC}$

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