DIRECTION: In the following questions, a statement of assertion (… - Vidyadip

MCQ

$\text{DIRECTION:}$ In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion: $A B C$ is an isosceles triangle with $A C=B C$. If $A B^2=2 A C^2$ then triangleltext $\{A B C\} $ is a right triangle.
Reason: If in atriangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
C
Assertion $(A)$ is true but reason $(R)$ is false.
D
Assertion $(A)$ is false but reason $(R)$ is true.

✓

Answer

Correct option: A.

Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.

We know that If in a triangle,
square of one side is equal to the sum of the squares of the other two sides,
then the angle opposite the first side is a right angle.
This is converse of Pythagoras theorem.

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