3/10/2024 0 Comments In parallelogram abcd find m∠a![]() ∠QRT = ∠PQR (alternate interior angles).PQ = RT (opposite sides of the parallelogram PQTR).To Prove: The diagonals PT and RQ bisect each other, i.e., PE = ET and ER = EQ.įirst, let us assume that PQTR is a parallelogram. PT and QR are the diagonals of the parallelogram. Theorem 3: Diagonals of a Parallelogram Bisect Each Other. We have to prove that ABCD is a parallelogram. Given: ∠A = ∠C and ∠B = ∠D in the quadrilateral ABCD.Īssume that ∠A = ∠C and ∠B = ∠D in the parallelogram ABCD given above. This proves that opposite angles in any parallelogram are equal.Ĭonverse of Theorem 2: If the opposite angles in a quadrilateral are equal, then it is a parallelogram. Thus, by ASA, the two triangles are congruent, which means that ∠B = ∠D. Let us assume that ABCD is a parallelogram. Given: ABCD is a parallelogram, and ∠A, ∠B, ∠C, ∠D are the four angles. Theorem 2: In a Parallelogram, the Opposite Angles are Equal. ![]() Therefore AB || CD, BC || AD, and ABCD is a parallelogram. Hence we can conclude that ∠BAC = ∠DCA, and ∠BCA = ∠DAC. Thus by the SSS criterion, both the triangles are congruent, and the corresponding angles are equal.
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