In an adjacent figure triangle ABC and triangle DBC are two triangles such that AB=BD and AC=CD Show that triangle ABC congruent triangle DBC?
since BC is common to both triangles, they are congruent by SSS
To prove that triangle ABC is congruent to triangle DBC, you can use the Side-Angle-Side (SAS) congruence criterion.
Here's how you can apply the SAS criterion to prove the congruence:
1. Start by stating the given information: In triangle ABC and triangle DBC, AB = BD and AC = CD.
2. Next, notice that both triangles share the same side, BC.
3. Now, let's look at the corresponding angles. Since triangle ABC and triangle DBC share the same base, BC, it implies that angle ABC and angle DBC have the same measure (as they are vertically opposite angles).
4. Finally, we have AB = BD and angle ABC = angle DBC. Applying the SAS criterion, we can conclude that triangle ABC is congruent to triangle DBC.
By following the SAS criterion, we have shown that the two triangles are congruent.