Triangles abc and dbc have the following characteristics: bc is a side of both triangles ∠acb and ∠dcb are right angles ac ≅ dc which congruence theorem can be used to prove △abc ≅ △dbc?
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The figure, in this case a triangle, is congruent if and only if the corresponding sides and angles are equal in measurement. In this case we have BC being common to both triangles. Thus, one pair of corresponding sides is equal. Next, we have another pair of corresponding sides that are equal, AC and DC. Lastly, we have the included angles being equal to each other. Thus, the congruence theorem that would best prove the congruence of the triangles is SAS that is Side-Angle-Side.

In triangles ABC and DBC, BC is a side of both triangles, ∠ACB and ∠DCB are right angles and AC ≅ DC. So, according to side angle side postulate triangle ABC and triangle DBC are congruent to each other.

Given :

According to the given data:

Therefore, according to the side angle side postulate triangle ABC and triangle DBC are congruent to each other. So, the correct option is D).

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