Question

Analyze the triangles shown. Steve determines that sides DK and BC are congruent. He also measures angles < K and < C and determines that they are congruent. He concludes that the triangles are congruent by the SAS Congruence Theorem. Is Steve correct? If he is incorrect, which congruence theorem should Steve use? Explain your reasoning and show all of your work including measurement of angles and/or line segments.

Answer 1

Sides DK and BC are congruent

Angles K and C are congruent

SAS = side angle side

The theorem states that the triangles with 2 equal sides, and also the angle between them.

But, we only know that the triangles have 1 equal side and one equal angle-

To use the ASA congruence theorem he should state that AC and EK are also congruent sides.