Question

what additional information do you need to prove $\triangle hmq cong \triangle pmq$ by sas
$\bigcirc hm cong pm$
$\bigcirc angle h cong angle p$
$\bigcirc hq cong pq$
$\bigcirc$ none of these, the triangles are not congruent

Explanation:

Step1: Recall SAS congruence rule

SAS requires 2 sides + included angle congruent.

Step2: Identify shared side

$\triangle HMQ$ and $\triangle PMQ$ share $\overline{MQ}$, so $\overline{MQ} \cong \overline{MQ}$.

Step3: Identify given congruent angles

$\angle HMQ \cong \angle PMQ$ (marked right angles).

Step4: Find missing SAS component

We need the second pair of sides forming the included angle: $\overline{HM} \cong \overline{PM}$.

Answer:

$\boldsymbol{HM \cong PM}$