Question

given: quadrilateral ABCD with ∠A= ∠C and BD the bisector ∠ABC 
prove: DB bisects ∠ADC

Answer 1

ΔABD ≡ ΔCBD ( L.U.U) because (BD)≡(BD), ∠A≡ ∠C , <ABD≡<CBD => <ADB ≡ <CDB =>DB bisects ∠ADC;