In parallelogram

MATHEMATICS · Single correct · CBSE · Mathematics · Triangles · Triangles

Problem

In parallelogram ABCDABCD, diagonal ACAC is drawn. Which reason best justifies why area(△ABC)=area(△CDA)\text{area}(\triangle ABC)=\text{area}(\triangle CDA)? (a) Both triangles lie on the same base ACAC and between the same parallels, so their areas are equal. (b) The triangles have equal corresponding angles and share side ACAC, making them congruent by ASA. (c) △ABC\triangle ABC and △CDA\triangle CDA are congruent by SAS. (d) The diagonal ACAC bisects the angles of the parallelogram, making the triangles similar and therefore equal in area.

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