Geometry
 Point: A fine dot on paper or a location on plane is called a point. A point has no length, breadth or thickness. Point is denoted by capital letters such as A, B or C etc.
 Line: The basic idea of line is staraightness. It has no breadth or thickness. It can be extended indefinitely in both directions. Line is denoted by small letters as l, m, n etc.
 Line Segment: Line segment is a part of line. It has two end points and a definite length.
 Ray: If a line segment is extended to unlimited length on one of the end point, we name it by a ray.
1) A line contains infinite points
2) Infinite lines can pass through a point
3) Two distinct lines in a plane can’t have more than one point common.
 Plane: A sheet of paper or surface of table has a flat surface. If we extend it in all directions to unlimited length, the extended flat surface is called a plane.
 Intersecting Lines: When two lines or line segments cross each other at a single point then they are called intersecting lines. When two lines intersect vertically opposite angles are equal.
And
 Parallel Lines: Lines that never intersect and are always at equal distance from each other are called parallel lines.
In the above figure –
are parallel lines.
Lines XY is called transversal
these angles are called alternate angles.
these angles are called corresponding angles.
Types of Angles
 Acute Angle: An angle which is less than is called an acute angle.
 Right Angle: An agnle of is called right angle.
 Obstuse Angle: An angle which is lying between and is called obtuse angle.
 Straight Angle: An angle of is called a straight angle.
 Reflex Angle: An angle which is lying between and is called is a reflex angle.
 Complete Angle: An angle of is called complete angle.
 Complementary Angle: Two angles whose sum is are called complementary angles.
 Supplementary Angle: Two angles whose sum is are called supplementary angle.
 Adjacent Angles: Two angles are said to be adjacent if they have a common arm and same vertex. In figure given below are adjacent angles
 Linear pair of Angles: Two adjacent angles form a linear pair of angle if their noncommon arms are two opposite rays. Sumof angles of linear pair is always .
 Triangle: A figure bounded by three line segments in a plane is called a triangle. It has three vertices, three sides and three angles.
Types of Triangles
 Acute Angled Triangle: when all three angles of triangle are acute then it is an acute angled triangle.
 Right Angled Triangle: When one angel of triangle then it is called right angled triangle.
 Obtuse Angled Triangle: When one angle of the triangle is obtuse angle then triangle is called obtuseangled triangle.
 Scalane Triangle: When all three sides of triangle are of different length then triangle is scalene triangle.
 Isoceles Triangle: When two sides of triangle are of equal length, then triangle is called isosceles. Two angles of isosceles triangle are also equal.
 Equilateral Triangle: It has all three sides of equal length. It has all three angles as .
Properties of Triangle
 Sum of three angles of a triangle ar are always .
 Sum of length of any two sides of a triangle is greater than the length of third side and difference of any two sides of a triangle is less than the third side.
 Side opposite to the greatest angle is the longest side.
 Sides opposite to equal angles are equal.
 The interior angles of a triangle (at each vertex) is equal to the sum of the two opposite interior angles.
 Congreuent Triangles: Two triangles are said to be congruent if all sides and angles of one triangles are equal to corresponding sides and angles of another triangle.
Conditions:
SideSideside: If all three sides of one triangle are equal to the corresponding sides of another triangle then the two triangles are congruent.
SideAngleSide: If two sides and included angle of one triangle are equal to the corresponding sides and included angle of another triangle then triangles are congreuent.
AngleSideAngle: If two angles and included side of the one triangle are equal to two angles and included side of another triangle then triangles ar congrucent.
RighthypotneuseSide: If hypotenuse and one side of a right triangle is equal to hypotenuse and one side of another right triangle then triangles are congruent.
 Similar Triangles: Two triangles are said to be similar if they are alike in shapes only. The corresponding angles of two similar triangles are equal but the corresponding sides are only proportional and not equal.
Conditions:
The three angles of one triangle are respectively equal to the three angles of the second triangle.
Two sides of one triangle are proportional to two sides of the other and the included angles are equal.
a) Ratios of sides = Ratio of heights = Ratio of medians = Ratio of angular bisectors
b) Ratio of area = Ratio of square of corresponding sides
 Medians: The line segment joining a vertex of triangle to mid point of opposite side is called median.
Medians of triangle pass through a common point which divides each median in 2 : 1
It two median of a triangle are equal then triangle is isosceles.  Altitude: A line segment from a vertex which is perpendicular to opposite side of triangle is called altitude.
The sum of any two medians of a triangle is greater than the third median.
In a right triangle the square of hypotenuse is equal to sum of the squares of perpendicular and base (Pythogoras Theorem).  Quadrilateral: Any four sided closed figure in a plane is called a quadrilateral. Sum of four angles of a quadrilateral is always .
 Trapezium: If one pair of opposite sides of a quadrilateral is parlled then it is called a trapezium.
 Parallelogram: A quadrilateral in which opposite sides are parallel is called a parallelogram.
In a Parallelogram –
1) Opposite sides are equal.
2) Opposite angles are equal.
3) Each diagonal divides the parallelogram into two congreuent triangles.
4) Sum of any two adjacent angels is .
5) Diagonals bisect each other.
 Rhombus: A rhombus is a parallelogram is which every pair of adjacent sides are equal. (i.e. all four sides are equal)
 Rectngle: A rectangle is a parallelogram in which all angles are .
Rectangle also satisfies all properties of parallelogram. In a rectangesl diagonals are equal.  Square: A square is a rectangle in which all four sides are equal.
All angles are
Diagonals are equal and bisect at right angle
When square inscribed in circle, diagonal becomes diameter of circle.
Circle
 A circle is a set of those points in a plane that are at a given constant distance from a given fixed point in the plane. The fixed point is O the centre and the given constant distance r is the radius.
 A B is called diameter where diameter =
 Chord is a line which joins any two points on the circle.
 In a circle, the perpendicular from the centre to a chord bisects the chord.
 In a circle, the line joining the centre of a circle to the midpoint of a chord is perpendicular to the chord.
 In a circle, equal chords subtend equals angles at the centre.
 In a circle, chords which subtend equal angles at the centre are equal.
 Equal chords of a circle are equidistant from the centre.
 Chords of a circle which are equidistant from the centre are equal.
The angle in a semicircle is a right angle. The converse of the above is also true and is very useful in number of cases.
Important Questions for Geometry
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Question 1 of 50
1. Question
1 pointsThe pair of adjacent angles in given figure is
Correct
Incorrect

Question 2 of 50
2. Question
1 pointsIf then measure of is
Correct
Incorrect

Question 3 of 50
3. Question
1 pointsIf then measure of is
Correct
Incorrect

Question 4 of 50
4. Question
1 pointsIf an angle is equal to its complementary angle then angle is
Correct
Incorrect

Question 5 of 50
5. Question
1 pointsIf supplementaryangles of an angle is then measure of the angle is
Correct
Let angle =
Then = 180
Incorrect
Let angle =
Then = 180

Question 6 of 50
6. Question
1 pointsRato of angles of a linear pair is 8 : 1 then measure of each angle is
Correct
Let angles be 8x and x
8x + x = 180
X =
Incorrect
Let angles be 8x and x
8x + x = 180
X =

Question 7 of 50
7. Question
1 pointsvalue of x in given figure is
Correct
6x + 7x + 5x =
X =
Incorrect
6x + 7x + 5x =
X =

Question 8 of 50
8. Question
1 pointsIf x = from given figure is
Correct
Z =
Incorrect
Z =

Question 9 of 50
9. Question
1 pointsValue of x + y in given figure is
Correct
Incorrect

Question 10 of 50
10. Question
1 pointsIf OP and OQ ar bisectors of
Correct
Incorrect

Question 11 of 50
11. Question
1 pointsIn given of figure if then value of x is
Correct
X =
Incorrect
X =

Question 12 of 50
12. Question
1 pointsIn given figure if p q and is
Correct
Incorrect

Question 13 of 50
13. Question
1 pointsIn given is p q and r s and is
Correct
Incorrect

Question 14 of 50
14. Question
1 pointsIn given ABCD, CDEF, is
Correct
Incorrect

Question 15 of 50
15. Question
1 pointsIn given figure ABCD, is
Correct
Incorrect

Question 16 of 50
16. Question
1 pointsIn given figure if then value of x is
Correct
y =
X =
Incorrect
y =
X =

Question 17 of 50
17. Question
1 pointsIn given figure is
Correct
Incorrect

Question 18 of 50
18. Question
1 pointsIf ratio of three angles of a triangle is 2 : 3 : 4 then measure of the angles is
Correct
Let angles be 2x, 3x and 4x then
2x + 3x + 4x =
9x = 180
X =
Incorrect
Let angles be 2x, 3x and 4x then
2x + 3x + 4x =
9x = 180
X =

Question 19 of 50
19. Question
1 pointsDiagonals of rectangle
Correct
Incorrect

Question 20 of 50
20. Question
1 pointsIn given figure if lm and is
Correct
Let
3x + 2x =
X =
Incorrect
Let
3x + 2x =
X =

Question 21 of 50
21. Question
1 pointsIn given figure OB and Oc are bisector of is
Correct
=
=
=
Incorrect
=
=
=

Question 22 of 50
22. Question
1 pointsIn given figure ABCD, then values of x and y is
Correct
x =
X + y =
Y =
Y =
Incorrect
x =
X + y =
Y =
Y =

Question 23 of 50
23. Question
1 pointsIn given figure if is
Correct
=
Incorrect
=

Question 24 of 50
24. Question
1 pointsThe complemenatary angle of angle is more than its thrice. The angle is
Correct
Let angle be
4x = 90 – 2 =
X =
Incorrect
Let angle be
4x = 90 – 2 =
X =

Question 25 of 50
25. Question
1 pointsRatio of an angle and its complementary angle is 2 : 3. The measure of each angle is
Correct
Let angles be
2x + 3x = 180
X = 36
Incorrect
Let angles be
2x + 3x = 180
X = 36

Question 26 of 50
26. Question
1 pointsIn given figure two lines AB and CD intersect at O. If is
Correct
=
Incorrect
=

Question 27 of 50
27. Question
1 pointsIf complementary angle is double of the angle then measure of angle is
Correct
Let angle be
X + 2x =
X =
Incorrect
Let angle be
X + 2x =
X =

Question 28 of 50
28. Question
1 pointsIn given figure is
Correct
=
Incorrect
=

Question 29 of 50
29. Question
1 pointsIn given figure is
Correct
2x + x =
X =
Incorrect
2x + x =
X =

Question 30 of 50
30. Question
1 pointsIn given figure is
Correct
= 180 
=
Incorrect
= 180 
=

Question 31 of 50
31. Question
1 pointsComplementary angle of the right angle is
Correct
Incorrect

Question 32 of 50
32. Question
1 pointsWhich side is the longest in given figure
Correct
Because angle opposite to BC is largest
Incorrect
Because angle opposite to BC is largest

Question 33 of 50
33. Question
1 pointsWhich angle is largest is given
Correct
Because side opposite to is the longest
Incorrect
Because side opposite to is the longest

Question 34 of 50
34. Question
1 pointsIn given figure, x + y
Correct
180  = y + 30
Incorrect
180  = y + 30

Question 35 of 50
35. Question
1 pointsIn given figure value of x + y + z is
Correct
180 – x + 180 + 180 – z =
X + y + z =
Incorrect
180 – x + 180 + 180 – z =
X + y + z =

Question 36 of 50
36. Question
1 pointsValue of x in given figure is
Correct
x = 55 + 30 + 50
=
Incorrect
x = 55 + 30 + 50
=

Question 37 of 50
37. Question
1 pointsIn given figure are then value of x is
Correct
= 110
X= (30 + 40) = 70
Incorrect
= 110
X= (30 + 40) = 70

Question 38 of 50
38. Question
1 pointsIn given then value of x is
Correct
Incorrect

Question 39 of 50
39. Question
1 pointsIn given figure if is
Correct
Incorrect

Question 40 of 50
40. Question
1 pointsIn given figure if l m then measure of is
Correct
x = 180 – 40 =
Incorrect
x = 180 – 40 =

Question 41 of 50
41. Question
1 pointsIn given figure if pq and then value of x is
Correct
=
X = 180 – 60 =
Incorrect
=
X = 180 – 60 =

Question 42 of 50
42. Question
1 pointsIn given figure PQ  RT, if is
Correct
=
Incorrect
=

Question 43 of 50
43. Question
1 pointsIn given figure if is
Correct
Incorrect

Question 44 of 50
44. Question
1 pointsIn given figure if p  q  r then measure of is
Correct
x =
X = 60 + 35
=
Incorrect
x =
X = 60 + 35
=

Question 45 of 50
45. Question
1 pointsIn given figure ABCD and ACEB the value of x + y is
Correct
X =
Y = 62
X + y = 60 + 62 =
Incorrect
X =
Y = 62
X + y = 60 + 62 =

Question 46 of 50
46. Question
1 pointsIn given figure if ABCDEF then value of x + y is
Correct
x = 180 – 38 =
Y =
X + y =
Incorrect
x = 180 – 38 =
Y =
X + y =

Question 47 of 50
47. Question
1 pointsIf lm then measure of x is
Correct
Incorrect

Question 48 of 50
48. Question
1 pointsIf pq then measure of y is
Correct
Incorrect

Question 49 of 50
49. Question
1 pointsIf lm and pq then measure of z is
Correct
Incorrect

Question 50 of 50
50. Question
1 pointsIf given figure then value of y is
Correct
Y – 90 + 50 = 180
Incorrect
Y – 90 + 50 = 180
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