Question

Two line segments PQ and RS intersect at point X in such a way that XP=XR and angle PSX=angle RQX.
Let's prove that triangle PXS is congruent with triangle RQX.
Pls hurry up .I need this answer as soon as possible.​
PLS..............

Answer 1

$\underline{\frak{refer \: to \: the \: image \: for \: figure}}$

$\underline{\huge{\frak{\red{question}}}}$

Two line segments PQ and RS intersect at point X in such a way that XP = XR and angle PSX = angle RQX.

Let's prove that ∆ PXS is congruent to ∆ RXQ.

$\underline{ \huge{ \red{ \frak{solution}}}}$

Consider

∆ PXS and ∆ RXQ

here,

PX = RX ( given)

angle PSX = angle RQX ( given)

and

angle PXS = angle RXQ ( vertically opposite angles)

so,

using AAS congruency criteria

∆ PXS is congruent to ∆ RXQ.