1. line AB = line CB : given
2. line BD = line BD ; Reflexive property
3. Line AD = line CD : congruent lines
4. Triangle ABD is congruent to Triangle BCD ( SAS postulate)
5. angle A = angle C ( corresponding angles)
Congruent triangles are triangles with thesame size and same corresponding angles.
To prove that angle A is congruent to angle C
1. line AB = line CB : given
2. line BD = line BD ; Reflexive property
3. Line AD = line CD : congruent lines of the quadrilateral
4. Triangle ABD is congruent to Triangle BCD ( SAS postulate)
5. angle A = angle C ( corresponding angles in the congruent triangles).