Answer:
Step-by-step explanation:
Given: 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.
To Prove: ΔAMN is an isosceles triangle. i.e any two sides in ΔAMN are
equal.
Solution: Now, In ΔADM and ΔADN
∠MAD=∠NAD ...(1) (∵Given)
AD=AD ...(2) (∵common side)
∠ADM=∠ADN ...(3) (∵Given)
Hence, from equation (1),(2),(3) ΔADM ≅ ΔADN
( ∵ ASA congruence rule)
⇒ AM=AN
Now, In Δ AMN
AM=AN (∵ Proved)
Hence, ΔAMN is an isosceles triangle.
