Question

can you prove these shapes are congruent?

Explanation:

Step1: Recall the definition of congruent shapes

Congruent shapes have the same shape and size.

Step2: Analyze the properties of the two quadrilaterals

Both are rectangles (all angles are right - angles). Let's assume the shorter side of the first rectangle \(EH = FG\) and the longer side \(EF=HG\). For the second rectangle \(VW = UT\) and \(VU = WT\). From the markings (equal - side markings), if we assume the side with one cross - mark has length \(a\) and the side with two cross - marks has length \(b\) for both rectangles.

Step3: Check the side - length equality

Since the side - length markings (one cross and two crosses) imply that the corresponding sides of the two rectangles are equal. For example, if in rectangle \(EFGH\), \(EH\) (with two cross - marks) and in rectangle \(VWUT\), \(VU\) (with two cross - marks) are equal, and \(EF\) (with one cross - mark) and \(VW\) (with one cross - mark) are equal. Using the Side - Side - Side - Side (SSSS) congruence criterion for quadrilaterals (in the case of rectangles, since all angles are \(90^{\circ}\), if the corresponding sides are equal), the two rectangles are congruent.

Answer:

yes