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Lydia has drawn quadrilateral ABCD with diagonal AC . According to her measurements, m∠DAC=m∠BCA and m∠DCA=m∠BAC . Without taking additional measurements, Lydia claims △ABC≅△CDA according to the ASA triangle congruence criteria. Explain why Lydia is correct.

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Answer:

Lydia is correct because the ASA criterion for triangle congruence states that if two triangles have two pairs of congruent angles and the common side of the angles in one triangle is congruent to the corresponding side in the other triangle, then the triangles are congruent which would prove her statement correct.

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