Question

are these shapes congruent?
(there are two quadrilaterals in the image, and two buttons: yes, no, and a submit button)

Explanation:

Step1: Match congruent sides

In quadrilateral \(FGHI\) and \(UXWV\), the marked sides (\(FI = XU\), \(FG = XW\)) are equal, and the other sides are corresponding.

Step2: Match congruent angles

Check angle pairs: \(\angle F = 63^\circ = \angle U\), \(\angle I = 117^\circ = \angle X\), \(\angle G = 90^\circ\) (right angle), while \(\angle W = 72^\circ\) (not 90°), \(\angle V = 108^\circ\) (not equal to any angle in \(FGHI\)).

Step3: Verify congruence condition

For quadrilaterals to be congruent, all corresponding sides and angles must match. Here, corresponding right angle and non-right angle do not match.

Answer:

no