Question

please answer my question
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Answer 1

Answer:

AD bisects ∠A and ∠D

Step-by-step explanation:

ΔABC is an isosceles triangle

∴AB = AC - (1)

BD = CD - (2)

Proof :

In ΔADC and ΔADB

side AC ≅ side AB - (from (1) )

side BD ≅ side CD - (from (2) )

Side AD ≅ side AD - (common side)

∴ ΔADC ≅ ΔADB  -  (By SSS test of congruency)

∴∠DAC ≅ ∠DAB  -  (corresponding angles of congruent triangles) - (3)

∴∠ADC ≅ ∠ADB  -  (corresponding angles of congruent triangles)  (4)

From (3) and (4)

AD bisects ∠A

AD bisects ∠D

∴ AD bisects ∠A and ∠D.

Hence Proved.