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

Question

TextRhombus as Special ParallelogramNCERT Textbook

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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.

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

CASE_STUDIESRhombus as Special Parallelogram

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.

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