Question

can you prove these shapes are congruent?
yes
no

Explanation:

Step1: Identify congruent sides

In quadrilateral $NKLM$:

• $NM = KL$ (single tick marks)
• $NK = ML$ (double tick marks)

In quadrilateral $STQR$:

• $ST = QR$ (single tick marks)
• $TS = RQ$ (double tick marks)

By matching tick marks, $NM=KL=ST=QR$ and $NK=ML=TS=RQ$, so all corresponding sides are equal.

Step2: Identify congruent angles

In $NKLM$: $\angle N=45^\circ$, $\angle M=135^\circ$, $\angle K=135^\circ$, $\angle L=45^\circ$
In $STQR$: $\angle T=45^\circ$, $\angle S=135^\circ$, $\angle Q=135^\circ$, $\angle R=45^\circ$
All corresponding angles are equal.

Step3: Apply congruence rule

For quadrilaterals, if all corresponding sides are equal and all corresponding angles are equal, the shapes are congruent (SSS congruence extended to quadrilaterals with matching angles confirming orientation).

Answer:

yes