Question

7 choose the options that best fit the blank boxes. (1 point) cpctc qm=rm sss congruence postulate definition of median pm=pm

Explanation:

Step1: Recall the concept of median

A median of a triangle is a line - segment that joins a vertex to the mid - point of the opposite side. If $PM$ is a median to side $QR$, then by the definition of median, point $M$ is the mid - point of $QR$, so $QM = RM$.

Step2: Recall the SSS (Side - Side - Side) congruence postulate

We know that $PQ=PR$ (given), $QM = RM$ (from the definition of median) and $PM = PM$ (common side). By the SSS congruence postulate, $\triangle PQM\cong\triangle PRM$.

Step3: Recall CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

Since $\triangle PQM\cong\triangle PRM$, then by CPCTC, $\angle Q=\angle R$.

Answer:

1. Definition of median: $QM = RM$
2. SSS Congruence Postulate: $\triangle PQM\cong\triangle PRM$ (using $PQ = PR$, $QM = RM$, $PM = PM$)
3. CPCTC: $\angle Q=\angle R$