Question

In the given figure, AB= AD and ∠BAC = ∠DAC (i) State the three pairs of matching parts used. (ii) Is ΔABC ≅ ΔADC? (iii) Which angle is equal to ∠BCA? (iv) Is ∠B = ∠D ? Why or why not​

Answer 1

Answer:

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DAC=∠BAC∠DCA=∠BCAAC=AC

(ii)

By ASA criterion, triangles are congruent.

(iii)

Since triangles are congruent hence, AB=AD because both sides originate from equal angles in two triangles.

(iv)

Since triangles are congruent hence,CD=CB because both sides originate from equal angles in two triangles.

Answer 2

Step-by-step explanation:

DAC=∠BAC∠DCA=∠BCAAC=AC

(ii)

By ASA criterion, triangles are congruent.

(iii)

Since triangles are congruent hence, AB=AD because both sides originate from equal angles in two triangles.

(iv)

Since triangles are congruent hence,CD=CB because both sides originate from equal angles in two triangles.