A two-column proof to prove that side BC is congruent with side DC should be completed as follows;
Statements Reasons
1. AC bisects ∠BAD 1. Given
2. ∠B ≅ ∠D 2. Given
3. ∠DAC ≅ ∠BAC 3. Definition of angle bisector
4. AC ≅ AC 4. Reflexive property
5. ∠ACB ≅ ∠ACD 5. ASA congruence property
6. BC ≅ DC 6. Definition of perpendicular bisector (C is the midpoint BD).
In Mathematics and Euclidean Geometry, an angle bisector is a type of line, ray, or segment, that typically divides or bisects a line segment exactly into two (2) equal and congruent angles.
Based on the definition of angle bisector, we can logically deduce that angle GFH is congruent with angle EFH;
m∠DAC ≅ m∠BAC
Based on the definition of a perpendicular bisector, we can logically deduce the following congruent sides;
BC ≅ DC