Question

question: 12 ingrid wants to prove that the diagonals of a parallelogram bisect each other, using the figure below. which statement and reason should be part of her proof? a. △qrs≅△rtq by sss b. △qrs≅△sqt by sss c. △qmr≅△smt by asa d. △qmr≅△tms by asa

Explanation:

Step1: Recall parallelogram properties

In parallelogram $QRTS$, $QR\parallel ST$ and $QS\parallel RT$. So, $\angle QRM=\angle SMT$ (alternate - interior angles) and $\angle RQM=\angle TSM$ (alternate - interior angles), and $QR = ST$ (opposite sides of a parallelogram are equal).

Step2: Apply congruence criterion

By the Angle - Side - Angle (ASA) congruence criterion, $\triangle QMR\cong\triangle SMT$. If these two triangles are congruent, then $QM = SM$ and $RM=TM$, which helps in proving that the diagonals of the parallelogram bisect each other.

Answer:

C. $\triangle QMR\cong\triangle SMT$ by ASA