What can you say about the angles at ∠ ADC and ∠ DAB?
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Practice makes perfect
If we can show that △ ABD≅ △ ADC, then we know that AC ≅ DB. Examining the diagram, we see that AD is a side that's shared by both triangles. By the Reflexive Property of Congruence, we know this side is congruent in both triangles. Let's mark this in our diagram.
Also, since AB∥ CD, and if we view AD as a transversal, we can claim that ∠ ADC and ∠ DAB are congruent by the Alternate Interior Angles Theorem.
Since we know two angles and a non-included side, we can by the AAS Congruence Theorem prove that the two triangles are congruent. Thus, we know that AC ≅ DB as corresponding parts of congruent triangles are congruent.
