Step-by-step explanation:
Step 1: Given
BD bisects ∠ADC
Step 2: Given
BD ⊥ AC
Step 3: Corresponding Parts of Congruence Triangles are Congruent
∠1 ≅ ∠2
Step 4: By definition of perpendicular
∠ABD = ∠CBD = 90° (BD ⊥ AC )
∠3 and ∠4 are right angles.
Step 5: By CPCTC,
∠3 ≅ ∠4
Step 6: Reflexive postulate
Any side or angle is reflexive to itself.
DB ≅ DB
Step 7: ASA postulate
∠1 ≅ ∠2 (A), DB ≅ DB (S) and ∠3 ≅ ∠4 (A),
∴ ΔABD ≅ ΔCBD (by ASA)
Step 8: By Corresponding Parts of Congruence Triangles are Congruent
DA ≅ DC
Step 9: Opposite sides of a triangle are equal.
ΔACD is isosceles.
Hence proved.
