Question

From the information given, determine which triangles, if any, are congruent and state by which rule. If the triangles cannot be shown to be congruent, write, "Cannot be determined" and explain.

Answer 1

Triangles ΔADM and ΔUTM are congruent by SAS postulate.

Explanation:

We say that two triangles are congruent if and only if they have exactly the same three sides and exactly the same three angles. So if you can turn one triangle into the other by moving, rotating or flipping, then they are definitively congruent. The symbol we use for expressing congruency is ≅. Since triangles ΔADM and ΔUTM have two matching sides and a matching angle between them, then they are congruent by SAS Postulate (Side Angle Side). Then:

ΔADM ≅ ΔUTM