Question

are these shapes congruent? yes no

Explanation:

Step1: Check the side lengths

In the first shape \(LMNK\), the side lengths are \(LM = 34\) mi, \(MN=46\) mi, \(NK = 49\) mi, \(KL = 19\) mi. In the second shape \(WXYV\), the side lengths are \(WX = 34\) mi, \(XY = 46\) mi, \(YV=49\) mi, \(VW = 19\) mi. So the side - lengths are equal.

Step2: Check the angle measures

In the first shape \(LMNK\), the angle measures are \(\angle L=121^{\circ}\), \(\angle M = 84^{\circ}\), \(\angle N=60^{\circ}\), \(\angle K = 95^{\circ}\). In the second shape \(WXYV\), the angle measures are \(\angle W=121^{\circ}\), \(\angle X = 84^{\circ}\), \(\angle Y=60^{\circ}\), \(\angle V = 95^{\circ}\). So the angle - measures are equal.

Since all corresponding side lengths and angle measures are equal, the two shapes are congruent.

Answer:

yes