Given:▱ABCD with diagonal line segment BD
Prove: Triangle ABD is congruent to triangle CDB
Statements:
1. ▱ABCD is a quadrilateral.
2. BD is a diagonal line segment of quadrilateral ABCD.
3. Point B is a common vertex of triangle ABD and triangle CDB.
4. Line segment AB is congruent to line segment CD. (Given)
5. Line segment BD is congruent to itself. (Reflexive Property)
6. △ABD and △CDB have a common side BD (common side).
7. △ABD and △CDB have two congruent sides. (Statements 4 and 6)
8. △ABD and △CDB have an included angle at point B. (Given)
9. △ABD is congruent to △CDB. (SSA Congruence)