Question

quiz: geometry a im (sequential) / 4.3 congruence 1. which congruence statement is correct for these triangles? o △abc≅△dbc o △abc≅△dcb o △abc≅△cbd o △abc≅△bdc

Explanation:

Step1: Identify congruent parts

We have right - angles at B, BC is common to both triangles, and another pair of sides are congruent (marked with cross).

Step2: Determine congruence statement

By Hypotenuse - Leg (HL) congruence criterion for right - triangles or Side - Angle - Side (SAS) if considering the right - angle as the included angle, the vertices must be named in corresponding order. In \(\triangle ABC\) and \(\triangle DCB\), the right - angles are at B, BC = CB (common side), and the other congruent sides match up with the correct vertex order.

Answer:

\(\triangle ABC\cong\triangle DCB\)