Geometry for SSC CGL Exam
Geometry for SSC Exam, IBPS SO, RRB and government exam preparation.
Angles An angle is a measurement of rotation of a line about a fixed point
The fixed point is called the vertex of an angle.
Angle is generally measured in degree
We read it as angle AOB
Types of angles
Acute angle If an angle is less than 90°, then it is called an acute angle
Right angle if an angle is equal to 90°, then it is called right angle
Obtuse angle If an angle is greater than 90° but smaller than 180°, then it is called an obtuse angle
Straight angle If an angle is equal to 180°, then it is called a straight angle
Reflexive angle If an angle is greater than 180° and smaller than 360°, then it is called reflexive angle
Complete angle If an angle is equal to 360°, then it is called complete angle
Complementary angles Two angles are called complementary if their sum is equal to 90°
Supplementary angles Two angles are called supplementary if their sum is equal to 180° or equal to two right angles.
Transverse lines when two lines intersected by a third line then the third line is called transverse line
Corresponding angles If the lines are parallel then their corresponding angles are equal and if the corresponding angles are equal then the lines are parallel
Corresponding angles is in the form of F
Alternate angle if the lines are parallel then their alternate angles are equal and its converse is also true
Alternate angle is in the form of Z
Vertically opposite angles when two lines intersect each other then the angles made at their intersection point are called vertically opposite angles.
These angles are in the form of X
Triangle A plane figure bounded by three straight lines is called a triangle
- A triangle has 3 angles
- The sum of angles of a triangle is 180°
Scalene triangle A triangle whose all sides are of different length
Geometry for SSC Exam
Isosceles triangle A triangle whose at least two sides are equal
Equilateral triangle a triangle whose all sides are equal
In equilateral triangle all angles are 60°
Right angled triangle A triangle in which an angle is equal to 90°
Pythagoras theorem In a right angled triangle AB2 + BC2 = AC2
Its converse is also true i.e. AB2 + BC2 = AC2, then the triangle is right angled triangle.
Acute angled triangle If all the angles of a triangle are acute angle, Then there is acute angled triangle.
Obtuse angled triangle If one angle of a triangle is obtuse, then there is obtuse angled triangle.
Median The median is a line segment joining a vertex to the mid_point of opposite sides.
Centroid The intersection point of medians is called centroid.
All the medians are concurrent i.e. they intersect each other at same point
Centroid divides the median into 2:1.
Orthocentre the intersection of altitudes drawn from vertex to its opposite sides is called orthocentre.
All the altitudes are concurrent.
Incentre The intersection point of angle bisector is called the incentre.
All the angle bisectors are concurrent.
Incircle is the centre of largest circle that can be inscribed in a triangle.
Circumcenter The intersection point of perpendicular bisector of any two sides of a triangle is called the circumcentre.
- All the perpendiculars bisectors are concurrent
- Circumcenter is the radius of largest circle that is outside the triangle and touch the vertices of triangle
Some important results on triangle
- If a side of a triangle is produced then the angle so formed is called exterior angle and is equal to the sum of opposite interior angles
- The sum of exterior angles of a triangle is equal to 360
- The sum of two sides of a triangle is always greater than the third side
- The angle opposite to greater side of a triangle is greater i.e. if AB > BC > CA, then angle C > angle A > angle B and conversely
- If any two sides of a triangle are equal, then the angles opposite to them are also equal and conversely
- Centroid divides the median of a triangle in 2:1
- In equilateral triangle centroid, orthocentre, incentre and circumcentre coincides i.e. they lie on the same point
- The line joining the mid_ points of two sides of a triangle is parallel to the third side
- Let ABC is a right angled triangle, right angle at B and D is the mid_ point of AC . then BD = ½ AC
- Let the bisector of angle B and angle C intersect each other at a point O.
Then angle BOC = 90 + ½ A
If ABC is a triangle and line BC is produced to D and AL is the bisector of angle A, then Angle ABC + angle ACD = 2 ( angle ALC)
Congruent triangles Two triangles are said to be congruent if they are the same triangle with different rotation i.e. they are of same size (all angles and all sides are equal)
If ABC is congruent to DEF we written this as ABCDEF
Every triangle is congruent to itself