As shown in the figure:
AB || CD
AD || CB
We need to prove AB = CD
So, the proof will be as follows:
Statements Reasons
0. AB || CD Given
,
1. m∠BAC = m∠DCA Alternate angles are congruent
,
2. AD || CB Given
,
3. m∠BCA = m∠DAC Alternate angles are congruent
,
4. AC = CA Reflexive property
,
5. ΔBAC ≅ ΔDCA By A.S.A [angle-side-angle] postulate
,
6. AB ≅ CD CPCTC