Question

(a) DA bisects $\angle BAC$ and $\angle B=\angle C$. Prove that $\Delta BDA\cong \Delta CDA$.

(b) If these triangles are congruent, choose the property by which they are congruent.

[4 MARKS]

Answer 1

Each Part: 2 Marks

(a)

In $\Delta BDAand\Delta CDA$

$\angle B=\angle C$ [Given]

$\angle BAD=\angle CAD$ [Given, DA is an angle bisector ]

$AD=AD$ [Common side]

$\Rightarrow \Delta BDA\cong \Delta CDA$ [ AAS criteria]


(b) we observe that in the given figures, there are no pairs of congruent sides. Since all of the congruency theorems call for at least one pair of congruent sides, there isn't enough information to prove that the triangles are congruent. Two triangles cannot be proved congruent just by AAA because triangles with same angles can have different sizes.