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dn = nc (as n is d mid point of dc) angle mnd = angle mnc (as mn perpendicular to dc) mn = mn (common side)

by s.a.s. axiom Δdnm congruent to Δcnm

since Δdnm congruent to Δcnm dm=cm

2) Δadb Δadc angle adb = angle adc (ad perpendicular to bc) angle dab = angle dac (given) ad = ad (common side) by a.s.a. axiom Δadb congruent to Δadc therefore angle abd = angle acd(corresponding angles of Δadb n Δadc) therefore abc is a isosceles triangle

3) Δabd Δacd ab = ac ad = ad angle adb = angle adc

by s.a.s. axiom Δabd congruent to Δacd

angle b = angle c ( corresponding angles of Δabd n Δacd) ad bisects bc since Δabd congruent to Δacd