A diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus.

Question

TextRhombus as Special ParallelogramNCERT Exemplar

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ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD. Show that (i) ∆ APB ≅ ∆ CQD (ii) AP = CQ

TextCongruence of TrianglesRhombus as Special ParallelogramMid-point Theorem for Triangle

Show that the diagonals of a rhombus are perpendicular to each other.

Diagonal AC of a parallelogram ABCD bisects ∠ A. Show that (i) it bisects ∠ C also, (ii) ABCD is a rhombus.

Diagonals of a rhombus are equal and perpendicular to each other. Is this statement true? Give reason for your answer.

ABCD is a rhombus in which altitude from D to side AB bisects AB. Find the angles of the rhombus.