Answer:
Step-by-step explanation:
<em><u>Given</u></em><u>:</u>       A line m is perpendicular to the angle bisector of ∠A. We call this  
                  intersecting point as D. Hence, in figure ∠ADM=∠ADN =90°.
                  AD is angle bisector of ∠A. Hence, ∠MAD=∠NAD.
<u><em>To Prove</em></u>:   <em><u>ΔAMN is an isosceles triangle. i.e any two sides in ΔAMN are</u></em>
<em>                    </em><em><u>equal. </u></em>
<em><u>Solution</u></em>:  Now, In ΔADM and ΔADN
                  ∠MAD=∠NAD     ...(1) (∵Given)
                   AD=AD                ...(2) (∵common side)
                   ∠ADM=∠ADN     ...(3) (∵Given)
                   <u><em> Hence, from equation (1),(2),(3) ΔADM ≅ ΔADN</em></u>
                                                          ( ∵ ASA  congruence rule)
                   ⇒<u><em> AM=AN</em></u>
                   Now, In Δ AMN 
                  AM=AN (∵ Proved) 
                   Hence, ΔAMN is an isosceles  triangle.