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In Fig. lines AB and CD intersect at O. If AOC + BOE = 70° and BOD = 40°, find BOE and reflex COE.

Given AB and CD are straight lines. ∠AOC + ∠BOE = 70° ------(i) ∠BOD = 40° -------(ii) AB is a straight... View Article

If (1, 2) , (4, y) , (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

Let A,B,C and D be the points of a parallelogram : A(1,2), B(4,y), C(x,6) and D(3,5). Since the diagonals of a parallelogram bisect each... View Article

How many litres of milk can a hemispherical bowl of diameter 10.5cm hold? (Assume π = 22/7)

Given Diameter of hemispherical bowl = 10.5 cm Radius of hemispherical bowl, r = 10.5/2 cm = 5.25 cm Formula Volume of the... View Article

AD and BC are equal perpendiculars to a line segment AB (see Fig.) . Show that CD bisects AB.

Solution Given AD and BC are equal perpendiculars to a line segment AB To Prove CD bisects AB Proof Two triangles ΔAOD and ΔBOC ∠ AOD = ∠... View Article

Find the coordinates of the point which divides the join of (- 1, 7) and (4, – 3) in the ratio 2:3.

Given, the line joining two points (-1, 7) and (4, -3) is divided by a point in the ratio of 2:3. Let us assume that P(x, y) be the required... View Article

In Fig., ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.

(i) From the diagram we observe that trapezium ABCD and triangle PCD have a common base CD and these are lying between the same parallel... View Article

In a right triangle ABC, ∠B = 90°. a. If AB = 6 cm, BC = 8 cm, find AC b. If AC = 13 cm, BC = 5 cm, find AB

Solution (a) In right triangle ABC According to Pythagoras Theorem AC2 = AB2 + BC2 AC2 = 62 + 82... View Article

How will you describe the position of a table lamp on your study table to another person?

To describe the position of a table lamp on your study table to another person we follow the given set[s From the figure given below... View Article

Find the area of the quadrilateral whose vertices, taken in order, are (-4, -2) , (-3, -5) , (3, -2) and (2, 3) .

Let the vertices of the quadrilateral be A (- 4, – 2), B ( – 3, – 5), C (3, – 2), and D (2, 3). Join AC and divide the... View Article

Find the distance between the following pairs of points: (i) (2, 3) , (4, 1) (ii) (-5, 7) , (-1, 3) (iii) (a, b) , (- a, – b)

The distance formula to find the distance between two points (x1, y1) and (x2, y2) is, say d, D = √[(x2 – x1)2 +... View Article

Construct an angle of 45° at the initial point of a given ray and justify the construction.

Procedure To construct an angle of 45°, the given steps can be followed 1. Let us draw a ray OA 2. Considering O as a centre with... View Article

Construct an angle of 90° at the initial point of a given ray and justify the construction.

Procedure To construct an angle of 90°, the given steps can be followed 1. Draw a ray OA 2. Considering O as the centre with any... View Article

Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540cm. Find its area.

Given The ratio of the sides of the triangle is given as 12: 17: 25 Perimeter is 540 cm Find out We have to determine the area of a triangle... View Article

Explain how a square is. (i) a quadrilateral (ii) a parallelogram (iii) a rhombus (iv) a rectangle

(i) a quadrilateral Solution A square is a quadrilateral, as it has four equal sides. (ii) a parallelogram Solution A square is a... View Article

The squares of which of the following would be odd numbers? i) 431 ii) 2826 iii) 7779 iv) 82004

Solution The square of an odd number will be an odd number, and the square of an even number will be an even number. i. The square of 431... View Article

Identify all the quadrilaterals that have. (a) four sides of equal length (b) four right angles

(a) four sides of equal length Solution: Rhombus and square have all sides equal. (b)four right angles Solution: Square and... View Article

In Fig, if lines PQ and RS intersect at point T, such that PRT = 40°, RPT = 95° and TSQ = 75°, find SQT.

∠PRT = 40°, ∠RPT = 95° and ∠TSQ = 75° From △PRT. ∠PRT +∠RPT + ∠PTR = 180° (The Sum of all the angles of Triangle is 180°) ⇒ ∠PTR = 45° Now... View Article

Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

Given AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm. Find out We have to determine the area of quadrilateral Solution we can... View Article

Find the ratio in which the line segment joining the points (-3, 10) and (6, – 8) is divided by (-1, 6) .

Let us assume the ratio in which the line segment joining ( -3, 10) and (6, -8) is divided by point ( -1, 6) be k :1. Therefore, -1 = (... View Article

Find the values of y for which the distance between the points P (2, – 3) and Q (10, y) is 10 units.

Distance between (2, – 3) and (10, y) is 10. Using distance formula, BC= √[(10 – 2)2 + (y... View Article