In the adjacent figure ABCD is a parallelogram ABEF is a rectangle show that ∆AFD ≅ ∆BEC.

Given :- ABCD is a parallelogram and ABEF is a rectangle

Formula used :-

SAS congruency rule

If two sides of triangle and angle made by the 2 sides are equal then both the triangles are congruent

Solution :-

In ∆AFD and ∆BEC

*AF=BE [opposite sides of rectangle are equal]

*AD=BC [opposite sides of parallelogram are equal]

As angle of rectangle is 90°

∠ DAB +∠ FAD=90°

∠ DAB=90° - ∠ FAD -----1

Sum of corresponding angles of parallelogram is 180°

∠ DAB+∠ ABC =180°

∠ DAB+∠ ABE+∠ EBC=180°

90° - ∠ FAD + 90° +∠ EBC=180° ∵ putting value from 1

180° +∠ EBC-∠ FAD=180°

∠ EBC - ∠ FAD=0

∠ EBC = ∠ FAD

⇒ Hence;

By SAS property both triangles are congruent

Conclusion :-

∆AFD ≅ ∆BEC