Question

in an isosceles triangle ABC, AB is equal to AC-DC and AD IS THE altitude to side BC .is triangle ABD congruent to ACD use two different ruels to prove it

Answer 1

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Answer 2

by sss nd sas
AD=AD(Common)
angle ADB= angle ADC(90°)
BD=CD(AD is an altitude)
therefore,∆ABD is congruent to ∆ACD (by SAS congruence condition)

∆ABC is an isosceles ∆(given)
hence, AB =AC
OR
∆ABD=~ ∆ACD (Proved above)
hence, AB=AC (by CPCT)
AD=AD (common)
BD=BC (AD is an altitude)
therefore, ∆ABD is congruent to ∆ACD (By SSS congruence condition)
Hence,Proved.