Statement -I: Two lines which pass through a | vedclass

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Question

(A) Let the two fixed lines be $L_1$ and $L_2$ intersecting at a point $P$.Any line $L$ passing through $P$ that is equally inclined to $L_1$ and $L_2

Vedclass · Accepted Answer

Both the Statements are true and Statement $-II$ is the correct explanation of the Statement $-I$.

Vedclass · Answer

(A) Let the two fixed lines be $L_1$ and $L_2$ intersecting at a point $P$.Any line $L$ passing through $P$ that is equally inclined to $L_1$ and $L_2$ must be an angle bisector of the angle formed by $L_1$ and $L_2$.There are two such angle bisectors (internal and external),which are always perpendicular to each other.Since the two lines described in Statement $-I$ are these two angle bisectors,they must be perpendicular.Thus,Statement $-I$ is true,Statement $-II$ is true,and Statement $-II$ correctly explains Statement $-I$.

Statement $-I$: Two lines which pass through a given fixed point and are equally inclined to two other lines passing through the same point,are always perpendicular to each other.
Statement $-II$: Angle bisectors of two intersecting lines are always perpendicular to each other.

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Statement $-I$: Two lines which pass through a given fixed point and are equally inclined to two other lines passing through the same point,are always perpendicular to each other.Statement $-II$: Angle bisectors of two intersecting lines are always perpendicular to each other.