Geometry handwritten notes pdf in Hindi for SSC GD

Hello Aspirants,

1. Points, Lines, and Planes:
   • A point is a location in space that has no size or dimension.
   • A line is a straight path with no endpoints that extends infinitely in both directions.
   • A plane is a flat surface that extends infinitely in all directions.
2. Angles:
   • An angle is formed when two rays share a common endpoint called the vertex.
   • Angles are measured in degrees (°) or radians (rad).
   • Types of angles include acute (less than 90°), right (90°), obtuse (greater than 90°), and straight (180°).
3. Triangles:
   • A triangle is a polygon with three sides and three angles.
   • Triangles can be classified based on their side lengths (equilateral, isosceles, scalene) and angle measurements (acute, right, obtuse).
4. Quadrilaterals:
   • A quadrilateral is a polygon with four sides and four angles.
   • Examples of quadrilaterals include squares, rectangles, parallelograms, rhombuses, and trapezoids.
5. Circles:
   • A circle is a set of points equidistant from a fixed point called the center.
   • Important concepts related to circles include radius, diameter, circumference, and area.
6. Polygons:
   • A polygon is a closed figure with three or more sides.
   • Polygons can be regular (all sides and angles are equal) or irregular (sides and angles vary).
7. Congruence and Similarity:
   • Two geometric figures are congruent if they have the same shape and size.
   • Two geometric figures are similar if they have the same shape but not necessarily the same size.
8. Pythagorean Theorem:
   • The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
9. Coordinate Geometry:
   • Coordinate geometry involves the use of coordinates to represent points, lines, and shapes on a coordinate plane.
   • The coordinates are given as ordered pairs (x, y), where x represents the horizontal distance (abscissa) and y represents the vertical distance (ordinate).
10. Geometric Transformations:
    • Geometric transformations include translations (slides), rotations (turns), reflections (flips), and dilations (scaling).
    • These transformations preserve certain properties of shapes, such as congruence and parallelism.

These are some key points about geometry, providing a basic understanding of fundamental concepts and principles. Geometry encompasses a wide range of topics, and further exploration can involve more advanced concepts like trigonometry, solid geometry, and analytical geometry.

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Most Important Geometry Question Answer

Q1. I is the incentre of ∆ABC, ∠ABC = 60° and ∠ACB = 50°. Then ∠BIC is
I , ∆ABC का अन्तःकेन्द्र है, ∠ABC = 60° और ∠ACB = 50°. तो ∠BIC का मान कितना है.
(a) 125
(b) 126
(c) 127
(d) 122

Q2. I is the incentre of ∆ABC, If ∠ABC = 60°, ∠BCA = 80°, then the ∠BIC is
I, ∆ABC का अन्तःकेन्द्र है, If ∠ABC = 60°, ∠BCA = 80°, तो ∠BIC का मान कितना है.
(a) 129
(b) 120
(c) 110
(d) 130

Q3. Let O be the in-center of a triangle ABC and D be a point on the side BC of ∆ABC, such that OD⊥BC. If ∠BOD = 15°, then ∠ABC =
O को त्रिभुज ABC का अंत:केंद्र है और D ΔABC की भुजा BC पर एक बिंदु इस प्रकार है कि, OD⊥BC  है.यदि ∠BOD = 5° है, तो ∠ABC =?
(a) 120
(b) 130
(c) 140
(d) 150

Q4. In ∆ABC, ∠B = 60° and ∠C = 40°. If AD and AE be respectively the internal bisector of ∠A and perpendicular on BC, then the measure of ∠DAE is
∆ABC में, ∠B = 60° और ∠C = 40°है. यदि AD और AE क्रमश: ∠A का आंतरिक द्विभाजक और BC पर लम्बवत्त है, तो ∠DAE का मान कितना है
(a) 10
(b) 20
(c) 30
(d) 40

Q5. The angle between the external bisectors of two angles of a triangle is 60°. Then the third angle of the triangle is
त्रिभुज के दो कोणों के बाहरी द्विभाजक के बीच का कोण 60 डिग्री है. तो त्रिभुज का तीसरा कोण कितना है?
(a) 40
(b) 60
(c) 50
(d) 70

Q6. In ∆ABC, the internal bisector of the ∠A, ∠B and ∠C intersect the circumcircle at x, y and z respectively. If ∠A = 50°, ∠CZY = 30° then ∠BYZ will be
ΔABC में, ∠A, ∠B और ∠C के आंतरिक द्विभाजक परिवृत्त पर क्रमश: x, y और z पर प्रतिच्छेद करते है. यदि  ∠A = 50 डिग्री, ∠CZY = 30 डिग्री है तो ∠BYZ कितना होगा?
(a) 35
(b) 45
(c) 55
(d) 65

Q7. Three sides of a ∆ABC are a = 30 cm, b = 57 cm, c = 33 cm. The internal bisector of ∠A meets BC at D, and the bisector passes through incentre O. The ratio AO : OD is–
ΔABC की तीन भुजा हैं, a = 30 सेमी, b = 57 सेमी, c = 33 सेमी  ∠A का आंतरिक द्विभाजक बी पर बीसी से मिलता है, और द्विभाजक ओसेन्ट्रे ओ के माध्यम से गुजरता है। अनुपात AO : OD है-
(a) 3:1
(b) 2:1
(c) 5:1
(d) 7:1

Q8. The circumcenter of a triangle ABC is O. If ∠BAC = 85° and ∠BCA = 75°, then the value of ∠OAC is
त्रिभुज ABC का परिकेंद्र O है. यदि ∠BAC = 85 डिग्री है और  ∠BCA = 75 डिग्री है, तो ∠OAC का मान कितना है?
(a) 70
(b) 80
(c) 90
(d) 100

Q9. If the length of the three sides of a triangle are 6 cm, 8 cm and 10 cm, then the length of the median to its greatest side is?
यदि त्रिभुज की तीन भुजाओं की लंबाई 6 सेमी, 8 सेमी और 10 सेमी है, तो सबसे लंबी भुजा की माध्यिका की लंबाई कितनी है?
(a) 2
(b) 6
(c) 4
(d) 5

Q10. O is the circumcenter of a triangle ABC whose ∠A = 50°. If bisector of ∠OBC and ∠OCB intersect at P then what is the measure of ∠BPC?
त्रिभुज ABC का परिकेंद्र O, ∠A = 50 डिग्री है यदि ∠OBC और ∠OCB का द्विभाजक P पर प्रतिच्छेद करता है तो ∠ BPC का माप कितना है?
(a) 140
(b) 160
(c) 130
(d) 150

Q11. Two medians AD and BE of ∆ABC interest at G at right angles. If AD = 9 cm and BE = 6 cm, then the length of BD (in cm) is
∆ABC की दो मध्यिका AD और BE, G पर समकोण पर प्रतिच्छेद करते है. यदि AD= 9 सेमी और BE = 6 सेमी है, तो BD (सेमी में) की लंबाई कितनी है
(a) 5
(b) 2
(c) 3
(d) 4

Q12. BL and CM are medians of ∆ABC right– angled at A and BC = 5 cm. If BL = (3√5)/2 cm, then the length of CM is
BL और CM, ∆ABC की मध्यिका है, जो A पर लम्बवत्त है और BC= 5 सेमी है. यदि BL= (3√5)/2 सेमी है, तो CM की लंबाई कितनी है
(a) 2√5 cm
(b) 3√5 cm
(c) 4√5 cm
(d) 5√5 cm

Q13. In a ∆ABC, BD & CE are the two medians which intersect each other at right angle. AB = 22, AC = 19, find BC = ?
एक ΔABC में, BD और CE की दो मध्यिका हैं जो एक-दूसरे को समकोण पर प्रतिच्छेद करते हैं. AB = 22, AC = 19, BC =? ज्ञात करें
(a) 13
(b) 12
(c) 14
(d) 15

Q14. In ∆ABC, BE, AD, CF is a median on AC, BC and AB respectively. AD = 10, BE = 6 and CF = 8 cm. Then find the area of ∆ABC?
ΔABC, BE, AD, CF क्रमशः AC, BC और AB पर एक मध्यिका है. AD= 10, BE= 6 और CF= 8 सेमी है. तो ΔABC का क्षेत्रफल कितना है?
(a) 32
(b) 33
(c) 34
(d) 35

Q15. O and C are respectively the orthocenter and the circumcenter of an acute angled triangle PQR. The points P and O are joined and produced to meet the side QR at S. If ∠PQS = 60° and ∠QCR = 130°, then ∠RPS = ?
O और C, न्यून कोण त्रिभुज PQR के क्रमशः ऑर्थोसेन्टर और परिकेंद्र हैं. बिंदु P और O जोड़ा जाता  हैं और इसे बड़ा कर भुजा QR, S पर मिलती हैं. यदि ∠PQS = 60 डिग्री और ∠QCR = 130 डिग्री, तो ∠RPS =?
(a) 35
(b) 36
(c) 37
(d) 38

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

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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