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Prove: △ABC≅△CDA. I really need help

Prove: △ABC≅△CDA. I really need help-example-1

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Answer:

AD ≅ BC | Given

AD || BC | Given

∠CAD ≅ ∠ACB | Alternate Interior Angles Theorem

AC ≅ AC | Reflexive Property of Congruence

△ABC ≅ △CDA | SAS Theorem

Explanation:

Since we know that AD and BC are parallel (given), we can think of the diagonal AC as a transversal to these parallel lines.

So, we can use the Alternate Interior Angles Theorem, which states that alternate interior angles are congruent. Hence, ∠CAD ≅ ∠ACB.

We also know that AC ≅ AC because of the Reflexive Property of Congruence.

Finally, we can use the SAS (side-angle-side) Theorem to prove the triangles congruent (△ABC ≅ △CDA) because we have two sides and an angle between them that we know are congruent.

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