Question

Δ ABC is isosceles with AB = AC. AD is the altitude from A on BC.

(i) Is ΔABD ≅ ΔACD?

(ii) State the pairs of matching parts you have used to answer (i).

(iii) Is it true to say that BD = DC?

Answer 1

(i) Yes, ΔABD ≅ ΔACD by RHS congruence condition.

(ii) We have used Hypotenuse AB = Hypotenuse AC

AD = DA

∠ADB = ∠ADC = 90° (AD ⊥ BC at point D)

(iii) Yes, it is true to say that BD = DC (corresponding parts of congruent triangles)

Since we have already proved that the two triangles are congruent.