Question

An isosceles right-angled triangle is reflected about its hypotenuse.

The figure formed by the triangle and its reflection is a

• A. Rhombus
• B. Square
• C. Rectangle
• D. Parallelogram

Answer 1

The correct option is B

Square

$△ABC$ is a right angled isosceles triangle right angled at $B$ in which $AB=BC$ and $AC$ is the hypotenuse.

Reflection of the triangle in the hypotenuse will result in another right angled isosceles triangle $ADC$ right angled at $D$ in which $AD=DC$ as shown in the figure:

If you combine both the triangles, you'll get a quadrilateral $ABCD$ in which $AB=BC=CD=DA$ and $\angle A=\angle B=\angle C=\angle D={90}^{\circ }$

Thus, the figure formed by the triangle and its reflection is a Square.