Question

ABCD is a rectangle and AC is a diagonal of the rectangle.
Show that the diagonal divides the rectangle into two
congruent triangles. Name the triangles and conditions
applied to prove that they are congruent.​

Answer 1

Here, ABCD is a rectangle.

AC is diagonal of a rectangle.

In △ABC and △CAD

⇒ AB=DC [ Opposite sides of rectangle ]

⇒ BC=AD [ Opposite sides of rectangle ]

⇒ AC=CA [ Common side ]

∴ △ABC≅△CAD [ By SSS congruence property ]

Answer 2

SOLUTION-

In ABC and CDA

Sides AB-CD (opposite side of rectangle)

B-D-90 degree each

Angles BC-DA

By SAS congruency

ABC is congruent to CDA