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Answer:
use the ASA postulate with alternate interior angles
Step-by-step explanation:
Congruence in general
For proving triangle congruence, there are basically 4 ways to do it. All require at least one side. They are ...
- SSS - 3 corresponding sides are shown to be congruent
- SAS - two corresponding sides and the angle between them are shown to be congruent
- ASA - two corresponding angles and the side between them are shown to be congruent (this one is used here)
- AAS - two corresponding angles and the side next to (a particular) one of them are shown to be congruent
When applied to right triangles, the right angle counts as one of the angles, and two sides determine the third, so these can become the LL, HL, HA, LA theorems, where the letters (H, L, A) stand for (hypotenuse, leg, angle), respectively.
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Approach to this problem
Of course, you're familiar with the relationship between angles where a line crosses parallel lines. Those relationships can help you identify two congruent angles in each triangle. The fact that the triangles share a side between those angles gives you a clue that you will be using the ASA postulate for your proof.
Specifics
1. AB ║ CD and AD ║ BC . . . . given
2. ∠1≅∠3 . . . . alternate interior angles at a transversal of parallel lines are congruent
3. AD≅DA . . . . reflexive property of congruence
4. ∠2≅∠4 . . . . alternate interior angles at a transversal of parallel lines are congruent
5. ∆DAB ≅ ∆ADC . . . . ASA postulate
