Question

1. determine if the triangles are congruent. if so, justify your answer using one of the triangle congruence postulates. if not, explain why not. 5. is ∠m≅∠q? how do you know?

Explanation:

Step1: Recall SSS congruence postulate

The SSS (Side - Side - Side) congruence postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. In the first pair of triangles, we can see that $\overline{AB}\cong\overline{EF}$, $\overline{BC}\cong\overline{FD}$, and $\overline{AC}\cong\overline{ED}$ (by the tick - marks on the sides). So, $\triangle ABC\cong\triangle EFD$ by SSS.

Step2: Recall CPCTC

CPCTC (Corresponding Parts of Congruent Triangles are Congruent). Since $\triangle MOP\cong\triangle QOP$ (by SSS as $\overline{MO}\cong\overline{QO}$, $\overline{OP}\cong\overline{OP}$ (common side), and $\overline{MP}\cong\overline{QP}$), then $\angle M\cong\angle Q$ because they are corresponding angles of congruent triangles.

Answer:

1. The triangles $\triangle ABC$ and $\triangle EFD$ are congruent by the SSS (Side - Side - Side) congruence postulate.
2. $\angle M\cong\angle Q$ because $\triangle MOP\cong\triangle QOP$ (by SSS) and by CPCTC (Corresponding Parts of Congruent Triangles are Congruent).