#### Chapters

Chapter 2 - Exponents of Real Numbers

Chapter 3 - Rationalisation

Chapter 4 - Algebraic Identities

Chapter 5 - Factorisation of Algebraic Expressions

Chapter 6 - Factorisation of Polynomials

Chapter 7 - Introduction to Euclid’s Geometry

Chapter 8 - Lines and Angles

Chapter 9 - Triangle and its Angles

Chapter 10 - Congruent Triangles

Chapter 11 - Co-ordinate Geometry

Chapter 12 - Heron’s Formula

Chapter 13 - Linear Equations in Two Variables

Chapter 14 - Quadrilaterals

Chapter 15 - Areas of Parallelograms and Triangles

Chapter 16 - Circles

Chapter 17 - Constructions

Chapter 18 - Surface Areas and Volume of a Cuboid and Cube

Chapter 19 - Surface Areas and Volume of a Circular Cylinder

Chapter 20 - Surface Areas and Volume of A Right Circular Cone

Chapter 21 - Surface Areas and Volume of a Sphere

Chapter 22 - Tabular Representation of Statistical Data

Chapter 23 - Graphical Representation of Statistical Data

Chapter 24 - Measures of Central Tendency

Chapter 25 - Probability

## Chapter 14 - Quadrilaterals

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Three angles of a quadrilateral are respectively equal to 110°, 50° and 40°. Find its fourth angle

In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1 : 2 : 4 : 5. Find the measure of each angles of the quadrilateral

In a quadrilateral ABCD, CO and DO are the bisectors of `∠`C and ∠D respectively. Prove that

`∠`COD = `1/2` (`∠`A+ `∠`B).

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

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Two opposite angles of a parallelogram are (3x – 2)° and (50 – x)°. Find the measure of each angle of the parallelogram .

If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram .

Find the measure of all the angles of a parallelogram, if one angle is 24° less than twice the smallest angle

The perimeter of a parallelogram is 22 cm . If the longer side measures 6.5 cm what is the measure of the shorter side?

In a parallelogram ABCD, ∠D = 135°, determine the measures of ∠A and ∠B

ABCD is a parallelogram in which ∠A = 70°. Compute ∠B, ∠C and ∠D .

In Fig., below, ABCD is a parallelogram in which ∠A = 60°. If the bisectors of ∠A and ∠B meet at P, prove that AD = DP, PC = BC and DC = 2AD.

In Fig. below, ABCD is a parallelogram in which ∠DAB **= **75° and ∠DBC = 60°. Compute

∠CDB and ∠ADB.

In below fig. ABCD is a parallelogram and E is the mid-point of side B If DE and AB when produced meet at F, prove that AF = 2AB.

**The following statement are true and false .**

In a parallelogram, the diagonals are equal

**The following statement are true and false. **

In a parallelogram, the diagonals bisect each other.

**The following statement are true and false .**

In a parallelogram, the diagonals intersect each other at right angles .

**The following statement are true and false .**

In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram.

**The following statement are true and false .**

If all the angles of a quadrilateral are equal, it is a parallelogram .

**The following statement are true and false .**

If three sides of a quadrilateral are equal, it is a parallelogram .

**The following statement are true and false . **

If three angles of a quadrilateral are equal, it is a parallelogram .

**The following statement are true and false . **

If all the sides of a quadrilateral are equal it is a parallelogram.

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In a parallelogram ABCD, determine the sum of angles ∠C and ∠D .

In a parallelogram ABCD, if `∠`B = 135°, determine the measures of its other angles .

ABCD is a square. AC and BD intersect at O. State the measure of ∠AOB.

ABCD is a rectangle with ∠ABD = 40°. Determine ∠DBC .

The sides AB and CD of a parallelogram ABCD are bisected at E and F. Prove that EBFD is a parallelogram.

P and Q are the points of trisection of the diagonal BD of a parallelogram AB Prove that CQ is parallel to AP. Prove also that AC bisects PQ.

ABCD is a square E, F, G and H are points on AB, BC, CD and DA respectively, such that AE = BF = CG = DH. Prove that EFGH is a square.

ABCD is a rhombus, EABF is a straight line such that EA = AB = BF. Prove that ED and FC when produced meet at right angles

ABCD is a parallelogram, AD is produced to E so that DE = DC and EC produced meets AB produced in F. Prove that BF = BC.

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In a ∆ABC, D, E and F are, respectively, the mid-points of BC, CA and AB. If the lengths of side AB, BC and CA are 7 cm, 8 cm and 9 cm, respectively, find the perimeter of ∆DEF.

In a triangle ∠ABC, ∠A = 50°, ∠B = 60° and ∠C = 70°. Find the measures of the angles of

the triangle formed by joining the mid-points of the sides of this triangle.

In a triangle, P, Q and R are the mid-points of sides BC, CA and AB respectively. If AC =

21 cm, BC = 29 cm and AB = 30 cm, find the perimeter of the quadrilateral ARPQ.

In a ΔABC median AD is produced to X such that AD = DX. Prove that ABXC is a

parallelogram.

In a ΔABC, E and F are the mid-points of AC and AB respectively. The altitude AP to BC

intersects FE at Q. Prove that AQ = QP.

In a ΔABC, BM and CN are perpendiculars from B and C respectively on any line passing

through A. If L is the mid-point of BC, prove that ML = NL.

In Fig. below, triangle ABC is right-angled at B. Given that AB = 9 cm, AC = 15 cm and D,

E are the mid-points of the sides AB and AC respectively, calculate

(i) The length of BC (ii) The area of ΔADE.

In Fig. below, M, N and P are the mid-points of AB, AC and BC respectively. If MN = 3 cm, NP = 3.5 cm and MP = 2.5 cm, calculate BC, AB and AC.

ABC is a triangle and through A, B, C lines are drawn parallel to BC, CA and AB respectively

intersecting at P, Q and R. Prove that the perimeter of ΔPQR is double the perimeter of

ΔABC

In Fig. below, BE ⊥ AC. AD is any line from A to BC intersecting BE in H. P, Q and R are

respectively the mid-points of AH, AB and BC. Prove that ∠PQR = 90°.

In Fig. below, AB = AC and CP || BA and AP is the bisector of exterior ∠CAD of ΔABC.

Prove that (i) ∠PAC = ∠BCA (ii) ABCP is a parallelogram

ABCD is a kite having AB = AD and BC = CD. Prove that the figure formed by joining the

mid-points of the sides, in order, is a rectangle.

ABC is a triang D is a point on AB such that AD = `1/4` AB and E is a point on AC such that AE = `1/4` AC. Prove that DE = `1/4` BC.

In below Fig, ABCD is a parallelogram in which P is the mid-point of DC and Q is a point on AC such that CQ = `1/4` AC. If PQ produced meets BC at R, prove that R is a mid-point of BC.

In the below Fig, ABCD and PQRC are rectangles and Q is the mid-point of Prove thaT

i) DP = PC (ii) PR = `1/2` AC

ABCD is a parallelogram, E and F are the mid-points of AB and CD respectively. GH is any line intersecting AD, EF and BC at G, P and H respectively. Prove that GP = PH

BM and CN are perpendiculars to a line passing through the vertex A of a triangle ABC. If

L is the mid-point of BC, prove that LM = LN.

Show that the line segments joining the mid-points of the opposite sides of a quadrilateral

bisect each other.

**Fill in the blank to make the following statement correct**

The triangle formed by joining the mid-points of the sides of an isosceles triangle is __ __

**Fill in the blank to make the following statement correct:**

The triangle formed by joining the mid-points of the sides of a right triangle is __ __

**Fill in the blank to make the following statement correct:**

The figure formed by joining the mid-points of consecutive sides of a quadrilateral is __ __