Nootan solutions for Mathematics [English] Class 9 ICSE chapter 11 - Rectilinear Figures [Latest edition]

Find the value of x and y from the following parallelogram:

Find the value of x and y from the following parallelogram:

The angles of a quadrilateral are in the ratio 2 : 3 : 3 : 4. Find the angles.

Three angles of a quadrilateral are in the ratio 7 : 8 : 11 and the fourth angle is of 100°. Find the angles.

Two adjacent angles of a parallelogram are 2x + 10° and 4x – 40°. Find the angles of the parallelogram.

Two opposite angles of the parallelogram are 3x – 5° and x + 45°. Find the angles of the parallelogram.

The angles of a quadrilateral are in the ratio 3 : 4 : 5 : 6. Show that it is a trapezium.

In the adjoining figure, ◻ABCD is a square and ΔABP is an equilateral triangle.

Find :

1. ∠AOB
2. ∠CPB
3. ∠PCD

In the adjacent parallelogram ABCD, AP ⊥ CD and AQ ⊥ BC. If x : y = 5 : 4, then find the angles of the parallelogram.

In the adjoining figure, ABCD is an isosceles trapezium in which AB || DC and AD = BС. If ∠ACD = 30° and ∠ADB = 25°, then find:

1. ∠AOD
2. ∠CBD

In the adjoining figure, OC = OD.

Find :

1. ∠CBD
2. ∠CAD
3. ∠BCA

In the adjoining figure, ABCD is a rhombus and ABE is an equilateral triangle. ∠BCD = 70°, find:

1. ∠ADE
2. ∠BDE
3. ∠BED

The diagonals of a rectangle ABCD intersect at P and PAL is an equilateral triangle such that B and L are on the same side of AC. If ∠ACD = 30°, find:

1. ∠ALB
2. ∠ABL

The diagonals of a quadrilateral ABCD bisect each other. If ∠A = 50°, then find ∠B.

The perimeter of a parallelogram ABCD is 48 cm. If BC = 3x – 2, DA = x + 2y + 2 and AB = 3y + 2, find the values of x and y.

In the parallelogram ABCD, E and F are the mid-points of AB and DC respectively. Prove that AEFD is a parallelogram.

In the adjoining figure, ABCD is a parallelogram. AX and CY are the bisectors of ∠A and ∠C respectively. 

Prove that :

1. ΔADX ≅ ΔCBY
2. AX || CY
3. AYCX is a parallelogram.

If a diagonal of a parallelogram bisects one of the angles of the parallelogram and it also bisects the opposite angle then prove that the two diagonals are perpendicular to each other.

In a square ABCD; A is joined to a point X on BC and D is joined to a point Y on AB. If AX = DY, prove that AX is perpendicular to DY.

In a rhombus ABCD, the altitude from D to side AB bisects AB. Find the angles of the rhombus.

If P and Q are points of trisection of the diagonal BD of a parallelogram ABCD, prove that : CQ || AP.

Prove that a diagonal of a rhombus bisects the angles at the vertices.

In ΔABC, median AD is produced to E such that AD = DE, prove that ABEC is a parallelogram.

In a quadrilateral ABCD, AB = AD and BC = CD.

Prove that :

1. AC bisects ∠BAD 
2. AC is the perpendicular bisector of BD.

In a parallelogram ABCD; BX is the bisector of ∠ABC and DY is the bisector of ∠ADC. Prove that BXDY is a parallelogram.

In a trapezium ABCD, the diagonals AC and BD intersect at point ‘O’, AB || DC and AD = BC.

Prove that :

1. ∠BAD = ∠ABC
2. ∠ADC = ∠BCD
3. AC = BD
4. OA = OB and OC = OD

Prove that the bisectors of interior angles of a parallelogram form a rectangle.

Prove that the bisectors of the interior angles of a rectangle form a square.

The side AB of a parallelogram ABCD is produced to X and the bisector of ∠CBX meets DA produced and DC produced at Y and Z respectively, prove that : DY = DZ = AB + BC.

ABCD is a rhombus. RABS is a straight line such that RA = AB = BS. Prove that RD and SC when produced meet at right angles.

The angles of a quadrilateral are in the ratio 3 : 3 : 5 : 7. The largest angle is ______.

The two adjacent angles of a parallelogram are in the ratio 3 : 7. The largest angle of the parallelogram is ______.

An angle of a parallelogram is half of its adjacent angle. The smallest angle of a quadrilateral is ______.

In the adjoining figure, ABCD is a parallelogram. If ∠CAD = 36° and ∠ABC = 110°, then ∠BAC is ______.

A quadrilateral ABCD is a trapezium with AB || DC if ______.

The sum of all four angles of a quadrilateral is ______.

If the diagonals of a quadrilateral bisect each other at right angle then it is a ______.

In a rectangle ABCD, the diagonals AC and BD intersect at O. If ∠OAB = 27°, ∠COD is equal to ______.

In the parallelogram ABCD, ∠A – ∠B – ∠C + ∠D is equal to ______.

The angle between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 55°. The largest angle of the parallelogram is ______.

In a quadrilateral ABCD, AO and BO are the bisectors of ∠A and ∠B respectively, then (∠C + ∠D) is equal to ______.