ABCD is a rhombus with \angle ABC = 110°. Its diagonals AC and BD meet at O, as shown. Find (a) \angle ADC, (b) \angle DAC, (c) \angle AOB.

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Rhombus as Special Parallelogram, Opposite Angles of Parallelogram are Equal | PadhAiPro

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TextRhombus as Special ParallelogramOpposite Angles of Parallelogram are Equal

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.

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

TextRhombus as Special Parallelogram

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.

In Fig.8.2, ABCD and AEFG are two parallelograms. If ∠C = 55º, determine ∠F.

In Fig.8.4, AX and CY are respectively the bisectors of the opposite angles A and C of a parallelogram ABCD. Show that AX || CY.