A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle.The triangles formed due to the diagonal of the rectangle are congruent to one another.
A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.
For the given rectangle ABCD, the length of the diagonals AC and BD can be written as,
AC = √(x² + y²)
BD = √(x² + y²)
Now, the triangles formed due to the diagonals AC and BD are ΔABC and ΔBCD. Also, for ΔABC and ΔBCD we can write,
∠ABC = ∠BCD = 90°
AB = CD = x {Oppsite sides of the rectangle are equal}
BC = AD = y {Oppsite sides of the rectangle are equal}
Hence, the two triangles are equal. Therefore, the triangles formed due to the diagonal of the rectangle are congruent to one another.
Learn more about Rectangle:
https://brainly.com/question/15019502
#SPJ1
