The diagonal AC of a quadrilateral ABCD bisects angle BAD and angle BCD. Prove that BC=CD.

BC = DC ⇒ proved

Step-by-step explanation:

* Lets explain how to solve the problem

- ABCD is a quadrilateral

- Its diagonal AC bisects angles BAD and BCD

- That means it divides the angle into two equal parts

∵ AC bisects angle BAD

∴ m∠BAC = m∠DAC

∵ AC bisects angle BCD

∴ m∠BCA = m∠DCA

* Lets revise a case of congruent we will use it to solve the problem

- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ

≅ 2 angles and the side whose joining them in the 2nd Δ

- In ΔABC and ΔADC

∵ m∠BAC = m∠DAC ⇒ proved

∵ m∠BCA = m∠DCA ⇒ proved

∵ AC is a common side in both triangles

∴ ΔABC ≅ ΔADC ⇒ by ASA

- From congruent

∴ AB = AD

∴ BC = DC ⇒ proved