Question

are these shapes congruent?
(image of two quadrilaterals: left one with vertices h, g, f, e, right angles at h, g, f, e, side gf = 46 ft, ef = 31 ft; right one with vertices t, u, v, s, right angle at t, angles at s=84°, v=97°, u=89°, sides st=31 ft, sv=46 ft, tu=46 ft, uv=26 ft)
options: yes, no

Explanation:

Step1: Analyze the first shape (EFGH)

The first shape (EFGH) is a rectangle (all angles are right angles, \(90^\circ\)) with sides \(31\) ft and \(46\) ft. So all angles are \(90^\circ\), and the side lengths are \(31\) ft, \(46\) ft, \(31\) ft, \(46\) ft.

Step2: Analyze the second shape (STUV)

The second shape (STUV) has angles \(84^\circ\), \(90^\circ\) (at T), \(89^\circ\), and \(97^\circ\). Let's check the sum of angles: \(84 + 90 + 89 + 97 = 360^\circ\) (which is correct for a quadrilateral). But the angles here are not all \(90^\circ\) (unlike the first shape). Also, the side lengths: \(31\) ft, \(46\) ft, \(26\) ft, \(46\) ft. The first shape has sides \(31\), \(46\), \(31\), \(46\) (so opposite sides equal, all angles \(90^\circ\)), while the second shape has a side of \(26\) ft (different from \(31\) ft) and non - right angles.

Step3: Compare for congruence

Congruent shapes must have all corresponding sides equal and all corresponding angles equal. The first shape is a rectangle (all angles \(90^\circ\), sides \(31, 46, 31, 46\)), the second shape has angles that are not all \(90^\circ\) and a side length of \(26\) ft (different from the first shape's corresponding side). So the shapes are not congruent.

Answer:

no