Question

can you prove these shapes are congruent? yes no

Explanation:

Step1: Identify congruent sides

In parallelogram $ABCD$: $AD=BC$, $AB=CD$. In parallelogram $FGHI$: $FI=GH$, $IH=FG$. The tick marks show $AD=FI$, $AB=IH$, so all corresponding sides are equal: $AD=FI$, $BC=GH$, $AB=IH$, $CD=FG$.

Step2: Identify congruent angles

In $ABCD$, $\angle A=\angle C$, $\angle B=\angle D$. In $FGHI$, $\angle I=\angle H$. The arc marks show $\angle A=\angle H$, $\angle B=\angle I$, so all corresponding angles are equal: $\angle A=\angle H$, $\angle B=\angle I$, $\angle C=\angle G$, $\angle D=\angle F$.

Step3: Apply congruence rule

For quadrilaterals, if all corresponding sides and angles are equal, the shapes are congruent (SSS + AA congruence for parallelograms, as matching sides and one pair of matching angles confirms full congruence).

Answer:

yes