Question

prove that the diagonals of a rectangle divide it in two congruent triangle

Answer 1

A rectangle is a quadrilateral whose interior angles are all equal.




✔️Properties of a rectangle :-

Property 1. Each of the interior angles of a rectangle is 90°.

Property 2. The diagonals of a rectangle bisect each other.

Property 3. The opposite sides of a rectangle are parallel.

Property 4. The opposite sides of a rectangle are equal.


✔️Proof:-

in rectangle ABDC

AD and CB are diagonals.

in ∆ABD and ∆DCA

➖AB=DC ( opposite sides of rectangle )
➖BD=CA ( opposite sides of rectangle )
➖AD=DA ( common )

so therefore,

∆ABD is congruent to ∆DCA by SSS congruency.....