Question

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

Explanation:

Step1: Recall median definition

If $PM$ is a median of $\triangle PQR$ and $M$ is on $QR$, by the definition of a median (a line - segment joining a vertex to the mid - point of the opposite side), if $M$ is the mid - point of $QR$, then $QM = RM$. So the reason for the statement "M is the mid - point of QR" is the definition of a median, and the statement for the reason "Definition of median" is $QM=RM$.

Step2: Identify reflexive property

The reflexive property of congruence states that a segment is congruent to itself. So for the reason "Reflexive Property of Congruence", the statement is $PM = PM$.

Step3: Determine congruence postulate

We know $PQ=PR$, $QM = RM$, and $PM=PM$. By the SSS (Side - Side - Side) congruence postulate, which states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent, $\triangle PQM\cong\triangle PRM$.

Step4: Use CPCTC

CPCTC (Corresponding Parts of Congruent Triangles are Congruent). Since $\triangle PQM\cong\triangle PRM$, then $\angle Q=\angle R$.

Answer:

1. QM = RM
2. Definition of median
3. PM = PM
4. SSS Congruence Postulate
5. CPCTC