Answer:
BC = DC ⇒ proved
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