Question

In $\Delta XYZ$, XM is the bisector of $\angle$ x and AB is perpendicular to XM, cutting it at D. Then which of the following relations hold true?

• A. $XD=DM$
• B. $YM=MZ$
• C. $XA=XB$
• D. $DM=BZ$

Answer 1

The correct option is C $XA=XB$

Since, $\angle YXM=\angle MXZ$

as, $XM$ is angle bisector.

and $\angle XDA=\angle XDB$ (Right angles)

and $DX$ is common side.

So, $△DXA=△DXB$ ($ASA$ criteria.)

Thus, $\angle DAX=\angle DBX$

So, $AX=BX$ (Sides opposite to equal angles are equal.)