Question

∆ ABC is isosceles with AB = AC. AD is the altitude from A on BC.
(i) Is ∆ ABD ≅ ACD?
(ii) State the pairs of matching parts you have used to answer (i).
(ii) Is it true to say that BD = DC?

Answer 1

(i)Yes, $△ABD\cong △ACD$ by RHS congruence condition.

(ii) We have used Hyp AB = Hyp AC
AD = DA
and $\angle ADB=\angle ADC=90°$ (AD$\perp$BC at point D)

(iii)Yes, it is true to say that BD = DC (c.p.c.t) since we have already proved that the two triangles are congruent.