If PQ || RS and ∠ONR = 30^o find ∠MON and hence ∠MOX .

In the Fig if ΔPQR ～ ΔXYZ, find a and b.

D is a point on the side BC. Such that \(\angle \)ADC = \(\angle \)BAC. Prove that \(\frac { CA }{ CD } =\frac { CB }{ CA } \) or CA² = CBXCD.

In the figure with respect to \(\triangle \)BEP and \(\triangle \)CPD prove that BP x PD = EP x PC.

Two triangles BAC and BDC right angled at A and D respectively are drawn on the same base BC and on the same side of BC. If AC and DB intersect at P. Prove that AP x PC = DP x PB.

Construct a quadrilateral DEAR with DE = 6 cm, EA = 5 cm, AR = 5.5cm, RD = 5.2 cm and DA = 10 cm. Also find its area.

Construct a quadrilateral NICE with NI = 4.5 cm, IC = 4.3 cm, NE = 3.5 cm, NC = 5.5 cm and IE = 5 cm. Also find its area

Construct a quadrilateral MATH with MA = 4 cm, AT = 3.6 cm, TH = 4.5 cm, MH = 5 cm and ∠A = 85°. Also find its area.

Construct a quadrilateral ABCD with AB = 7 cm, AD = 5 cm, CD = 5 cm, ∠BAC = 50° and ∠ABC = 60°. Also find its area.

Construct a quadrilateral PQRS with PQ = QR = 5 cm, ∠QPR = 50^o, ∠PRS = 40^o and ∠RPS = 80^o Also find its area.