if the diagonals of a parallelogram are equal, then show that it is a rectangle.

3

(a)

Diagonal AC of a parallelogram ABCD bisects \(\angle A\) (see figure). Show that:
(i) it bisects \(\angle C\) also
(ii) ABCD is a rhombus.

3

(a)

ABCD is a parallelogram and APand CQ are perpendiculars from vertices A and C on diagonal BD respectively. Show that:
\((i)\Delta APB\cong \Delta CQD\)
\(\\ (ii)AP=CQ\)

3

(a)

Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

3

(a)

The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.

3

(a)

In the given figure, ABCD is a rhombus. Find \(\angle CDB\)

3

(a)

Prove that the diagonals of a rectangle are equal in length.

3

(a)

PQRS is a parallelogram and PL and RM are perpendiculars drawn from the vertices P and R of the parallelogram on diagonal SQ. Show that
(i) ΔPQL ≡ ΔRMS
(ii) PL = RM

3

(a)

In the given figure, in a parallelogram ABCD, two points P and Q are taken on the diagonal BD such that DP = BQ. Show that:

(i) ΔAPD≡ΔCQB
(ii) ΔAQB≡ΔCPD
(iii) APCQ is a parallelogram.

3

(a)

In a parallelogram PQRS of the given figure, the bisectors of ㄥP and ㄥQ meet SR at  O. Show that ㄥPOQ=90°

3

(a)

ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Fig ). AC is a diagonal. Show that :
(i) SR || AC and SR \(=\frac{1}{2} \mathrm{AC}\)
(ii) PQ = SR
(iii) PQRS is a parallelogram

3

(a)

D, E and F are the mid-points of sides PQ, QR and RP respectively of an equilateral ΔPQR. Show that ΔDEF is also an equilateral triangle.

3

(a)

In given figure, ABCD is a parallelogram. P, Q are the mid-points of AB and DC. Show that:
(i) APCQ is a parallelogram.
(ii) DPBQ is a parallelogram.
(iii) PSQR is a parallelogram.

3

(a)