Question

∆ ABC is isoseles with AB = AC. Also, AD ⊥ BC meeting BC in D. Are the two triangles ABD and ACD congruent? State in symbolic form. Which congruence condtion do you use? Which side of ∆ ADC equls BD? Which angle of ∆ ADC equals ∠B?

Answer 1

We have AB = AC ......(1)
AD = DA (common)........(2)
and $\angle ADC=\angle ADB$ (AD$\perp$BC at point D)........(3)

Therefore from 1, 2 and 3, by RHS congruence condition,
$$\begin{gathered} \text{△ABD}\cong \text{△ACD} \\ \text{Now,}\text{the triangles are congruent}.\text{Therefore,}\text{BD}=\text{CD.} \\ \text{And}\text{∠ABD}=\text{∠ACD}\text{(c.p.c.t).} \end{gathered}$$