Question

can you prove these shapes are congruent? yes no

Explanation:

Step1: Identify given congruent sides

In quadrilateral \(ABCD\): \(AB = CD\), \(AD = BC\) (marked by tick marks). In quadrilateral \(JKLM\): \(JK = ML\), \(JM = KL\) (marked by tick marks). Also, the tick marks show \(AB = JK\), \(BC = KL\), \(CD = LM\), \(AD = JM\), so all corresponding sides are congruent: \(AB \cong JK\), \(BC \cong KL\), \(CD \cong LM\), \(AD \cong JM\).

Step2: Identify given right angles

All angles in both quadrilaterals are right angles (\(\angle A=\angle B=\angle C=\angle D = 90^\circ\), \(\angle J=\angle K=\angle L=\angle M = 90^\circ\)), so all corresponding angles are congruent.

Step3: Apply congruence rule for rectangles

For rectangles, if all corresponding sides are congruent, the rectangles are congruent (by SSS congruence extended to quadrilaterals, since all angles are fixed right angles).

Answer:

yes