Statement A (Assertion) : In figure, D E|| A C and D C|| A P. The… - Vidyadip

MCQ

Statement A (Assertion) : In figure, $D E|| A C$ and $D C|| A P$. Then $\frac{B E}{E C}=\frac{B C}{C P}$.

Statement $R$ (Reason) : If a line divides any two sides of a triangle in the same ratio, then the line must be parallel to the third side.

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

Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is not the correct explanation of assertion (A).

(b): As in $\triangle B A C, D E \| A C$
$\Rightarrow \frac{B D}{D A}=\frac{B E}{E C}$[By B.P.T]$\ldots(i)$
Also, in $\triangle B A P, D C \| A P$
$\Rightarrow \frac{B D}{D A}=\frac{B C}{C P} \quad$ [By B.P.T]$\ldots(ii)$
From (i) and (ii), $\frac{B E}{E C}=\frac{B C}{C P}$
Both (A) and (R) are true but (R) is not the correct explanation of (A).

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