Question

can you prove these shapes are congruent?

Explanation:

Step1: Recall the definition of congruent shapes

Congruent shapes have all corresponding sides and angles equal.

Step2: Check corresponding sides

From the markings (the red tick - marks), we can see that the sides of the two quadrilaterals \(LMNK\) and \(SPQR\) are equal. For example, if \(LM = SP\) (marked with one tick), \(MN=PQ\) (marked with two ticks), \(NK = QR\) (marked with one tick), and \(KL=RS\) (marked with two ticks).

Step3: Check corresponding angles

The angles (marked with red arcs) are equal. For example, \(\angle L=\angle P\), \(\angle K=\angle R\)

Answer:

Yes, the two shapes are congruent.