Geometry handwritten notes pdf in English for SSC CHSL

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Points: A point is a location in space that has no size or shape. It is represented by a dot and named using a capital letter. Lines: A line is a straight path that extends infinitely in both directions. It is represented by a straight line with arrows on both ends and named using any two points on the line.

Line segments: A line segment is a part of a line that has two endpoints. It is represented by a straight line with a bar above the two endpoints and named using the two endpoints. Rays: A ray is a part of a line that has one endpoint and extends infinitely in one direction. It is represented by a straight line with an endpoint and an arrow on the other end, and named using the endpoint and any other point on the ray. Angles: An angle is formed by two rays that share a common endpoint, called the vertex of the angle. It is measured in degrees and named using the vertex point. Triangles: A triangle is a closed figure with three sides and three angles. It is named using the vertices or the capital letters at each vertex.

Quadrilaterals: A quadrilateral is a closed figure with four sides and four angles. Some common types of quadrilaterals are square, rectangle, parallelogram, trapezoid, and rhombus. Circles: A circle is a closed figure in which all points on the boundary are equidistant from the center point. It is named using the center point. Perimeter: The perimeter of a figure is the total length of its sides. It is measured in units such as centimeters, meters, feet, or inches. Area: The area of a figure is the amount of space inside the figure. It is measured in square units such as square centimeters, square meters, square feet, or square inches.

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Most Important Geometry Plane & Solid Geometry

Plane geometry, also known as Euclidean geometry, is the branch of geometry that deals with two-dimensional figures in a flat or “plane” surface. These figures include points, lines, angles, triangles, circles, polygons, and other planar shapes. Plane geometry involves the study of their properties, relationships, and measurements, such as area, perimeter, and circumference.

Solid geometry, also known as three-dimensional geometry, is the branch of geometry that deals with three-dimensional shapes and figures in space. These figures include cubes, spheres, pyramids, cones, cylinders, and other solid shapes. Solid geometry involves the study of their properties, relationships, and measurements, such as volume, surface area, and cross-sectional area.

Both plane and solid geometry use many of the same concepts and principles, such as points, lines, angles, and geometric transformations. However, solid geometry involves additional concepts and techniques, such as spatial visualization and projection, which are not required in plane geometry. Both branches of geometry have numerous practical applications in fields such as architecture, engineering, physics, and computer graphics.

Most Important Geometry Question Answer

Q : Areas of two similar triangles are 36 cm2 and 100 cm2. If the length of a side of the larger triangle is 20 cm, then the length of the corresponding side of the similar triangle is:

(A) 15 cm

(B) 14 cm

(C) 12 cm

(D) 13 cm

Answer : C

Q : D and E are midpoints of side AB and AC respectively of the ΔABC. A line drawn from A meets BC at H and DE at K. AK : KH = ?
(A) 1 : 1

(B) 1: 2

(C) 2 : 1

(D) 3 : 2

Answer : A

Q : If the base radius of a right circular cylinder is reduced to half and its height remains the same, then the ratio of the volume of new formed cylinder to original cylinder would be:
(A) 1: 2

(B) 1: 1

(C) 2: 1

(D) 1: 2

Answer : B

Q : A piece of wire when bent to form a circle will have a radius of 84 cm. If the wire is bent to form a square, the length of a side of the square is
(A) 152 cm

(B) 132 cm

(C) 168 cm

(D) 225 cm

Answer : B

Q : A solid sphere of diameter 7 cm is cut into two equal halves. What will be the increase (in cm.2) in the total surface area?
(A)

(B)

(C)

(D)

Answer : B

Q : The largest and the second largest angles of a triangle are in the ratio of 3 : 2 respectively. The smallest angle is 20% of the sum of the rest two angles. What is the sum of the smallest and the second largest angles?
(A) 80°

(B) 60°

(C) 100°

(D) 90°

Answer : D

Q : If each interior angle is doubled of each exterior angle of a regular polygon with n sides, then the value of n is
(A) 3

(B) 6

(C) 5

(D) 8

Answer : B

Q : ∠A, ∠B, ∠C are three angles of a triangle. If ∠A -∠B =18°, ∠B – ∠C = 45°, then, ∠B, ∠A and ∠C are
(A) 69° ,88° , 24°

(B) 69°, 88°, 23°

(C) 69°, 87°, 24°

(D) 69°, 89°, 22°

Answer : C

Q : In ∆ABC, ∠B is a right angle, AC = 6cm, and D is the mid-point of AC. The length of BD is:
(A) 4 cm

(B) √6 cm

(C) 3 cm

(D) None of these

Answer : C

Q : Each exterior angle of a regular polygon measures 9°. How many sides does the polygon have?
(A) 36

(B) 45

(C) 40

(D) 30

Answer : C

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Most Important Geometry Question Answer

Q : A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. The area of the circle is:
(A) 125 cm2

(B) 230 cm2

(C) 550 cm2

(D) 616 cm2

Answer : D

Q : If the angles of a triangle are in the ratio of 1:4:7, then find the ratio of the greatest angle to the smallest angle.
(A) 7:2

(B) 2:3

(C) 7:1

(D) 3:5

Answer : C

Q : If the following figure, AC||BD, ∠CAF = 25o, ∠DBG = 65o and BF = BA, then ∠BFE is equal to –

(A)

(B)

(C)

(D)

Answer : B

Q : ‘G’ is centroid of ΔABC if AG = BC then find ∠BGC.
(A)

(B)

(C)

(D)

Answer : A

Q : In triangle ABC a straight line parallel to BC intersects AB and AC at D and E respectively. If AB = 2AD then DE : BC is
(A) 2 : 3

(B) 2 : 1

(C) 1 : 2

(D) 1 : 3

Answer : C

Q : ABCD is cyclic quadrilateral Sides AB and DC, when produced, meet at E, and sides BC and AD, When produced, meet at F. If ∠BFA=60° and ∠AED=30°, then the measure of ∠ABC is:
(A) 65°

(B) 70°

(C) 80°

(D) 75°

Answer : D

Q : P is a point outside a circle and is 26 cm away from its centre. A secant PAB drawn form P intersects the circle at points A and B such that PB=32 cm and PA=18cm. The radius of the circle (in cm) is:
(A) 12

(B) 13

(C) 10

(D) 8

Answer : C

Q : In the given figure, a circle is placed in a rectangle with another rectangle of dimension 10 cm × 5 cm whose one vertex coincides with vertex of bigger rectangle and opposite vertex lies on circumference of circle. Find the radius of circle.

(A) 35 cm

(B) 25 cm

(C) 40 cm

(D) 20 cm

Answer : B

Q : In ΔABC, AB=c cm, AC= b cm and CB=a cm, If ∠A=2 ∠B, then which of the following is true?
(A)

(B)

(C)

(D)

Answer : C

Q : In the figure below, find the value of AB.

(A)

(B)

(C)

(D)

Answer : B

Most Important Geometry Question Answer

Q : If the perimeter of a rhombus is 80 cm and one of its diagonals is 24 cm, then what is the are (in cm2) of the rhombus?
(A) 218

(B) 192

(C) 384

(D) 768

Answer : C

Q : PAB and PCD are two secants to a circle . If PA 10 cm , AB = 12 cm and PC = 11 cm , then what is the value ( in cm ) of PD ?
(A) 18

(B) 9

(C) 20

(D) 12

Answer : C

Q : In any triangle ABC, AB + BC = 12 cm, BC + CA = 14 cm and CA + AB = 18 cm. What will be length of radius of a circle, if the perimeter of circle is equal to the perimeter of triangle ABC?
(A) 2 cm

(B) 3.5 cm

(C) 1.5 cm

(D) None of these

Answer : B

Q : Triangle PQR is inscribed in a circle such that P, Q and R lies on the circumference . If PQ is the diameter of the circle and ∠PQR = 40 ° , then what is the value ( in degrees ) of ∠QPR ?
(A) 40

(B) 45

(C) 50

(D) 55

Answer : C

Q : In the given figure, SX is tangent. SX = OX = OR. If QX=3 cm and PQ = 9 cm. then what is the value (in cm) of OS?

(A) 6

(B) 5

(C) 4

(D) 3

Answer : D

Q : A circle with radius 42 cm is drawn. What will be length of arc of a sector subtending an angle of 60 degrees at the Centre?
(A) 44 cm

(B) 22 cm

(C) 66 cm

(D) 88 cm

Answer : A

Q : In the given figure ABC is an equilateral triangle. Two circles of radius 4 cm and 12 cm are inscribed in the triangle. What is the side (in cm) of an equilateral triangle?

(A)

(B)

(C) 24

(D)

Answer : D

Q : The area of a rhombus is 144 square units. The length of one of its diagonals is twice the length of other diagonal. What is the sum of length of its diagonals?
(A) 12 units

(B) 18 units

(C) 24 units

(D) 36 units

Answer : D

Q : If the area of a circle is 9π sq.cm then it circumference is
(A) 9 cm

(B) 6 π cm

(C) 3π cm

(D) 6 cm

Answer : B

Q : What is the measure of the circum radius of a triangle whose sides are 9cm, 40cm and 41cm?
(A) 6 cm

(B) 4 cm

(C) 20.5 cm

(D) 24.5 cm

Answer : C

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