What is the reason for the third step in this proof? Corresponding sides of congruent triangles are equal in length. The diagonals of a rectangle bisect each other. SSS criterion for congruence Opposite sides of a parallelogram are congruent.

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nmatungwa05 nmatungwa05 · Answer 1 · 2020-11-05T14:46:53+01:00

Answer: D Opposite sides of a parallelogram are congruent.

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shubhamchouhanvrVT shubhamchouhanvrVT · Answer 2 · 2022-06-08T12:07:13+02:00

The correct answer is the Opposite sides of a parallelogram are congruent.

A parallelogram is a quadrilateral having four sides and the two opposite sides are equal and parallel to each other.

Consider a parallelogram with diagonals that are congruent and perpendicular.

In triangles Δ AOB and Δ AOD,

OA = OA (common)

OB = OD (Since the diagonals of a parallelogram bisect each other)

∠ AOB = ∠ AOD = 90° (diagonals are perpendicular)

Therefore, Δ AOB ≅ Δ AOD (By SAS postulate)

Since, corresponding parts of congruent triangles are equal,

AB = AD

Similarly, we can prove

BC = CD and CD = DA

So, AB = BC = CD = DA.

Also, it is given that AC = BD.

Therefore the correct answer is the Opposite sides of a parallelogram are congruent.

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