Question
(a) DA bisects ∠BAC and ∠B=∠C. Prove that ΔBDA≅ΔCDA.
(b) If these triangles are congruent, choose the property by which they are congruent.
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[4 MARKS]
(b) If these triangles are congruent, choose the property by which they are congruent.
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  [4 MARKS]
Answer:
:
Each Part: 2 Marks
(a)
In ΔBDAandΔCDA
∠B=∠C [Given]
∠BAD=∠CAD [Given, DA is an angle bisector]
AD=AD [Common side]
⇒ΔBDA≅ΔCDA [ AAS criteria]
(b) we observethat 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'tenough 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.
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:
Each Part: 2 Marks
(a)
In ΔBDAandΔCDA
∠B=∠C [Given]
∠BAD=∠CAD [Given, DA is an angle bisector]
AD=AD [Common side]
⇒ΔBDA≅ΔCDA [ AAS criteria]
(b) we observethat 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'tenough 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.
Was this answer helpful ?
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