Question

are these shapes congruent?

Explanation:

Step1: Check the number of sides

The first shape is a pentagon (5 - sided polygon), and the second shape is also a pentagon.

Step2: Check the side - length correspondence

In the first pentagon \(JKLM\), the side - lengths are \(JK = 36\) in, \(KL=18\) in, \(LM = 18\) in, \(MM\) (assuming it's \(ML\)) is not relevant for comparison in terms of congruence (but we check all). In the second pentagon \(TUVW\), the side - lengths are \(TU = 36\) in, \(UV = 18\) in, \(VW=18\) in, \(WT = 29\) in. Since \(JM = 38\) in (from the first pentagon) and \(WT=29\) in (from the second pentagon), the side - lengths are not all equal.

Step3: Check the angle - measure correspondence

Even if we assume some angle - measure similarities (e.g., \(\angle K=\angle U = 82^{\circ}\), \(\angle J=\angle T=55^{\circ}\)), because of the non - matching side lengths (specifically \(JM
eq WT\)), the congruence condition (all corresponding sides and angles of two polygons must be equal for them to be congruent) is not met.

Answer:

No, the shapes are not congruent.