Geometry Question for SSC CGL
Sufficient condition for congruence of two triangles
- SAS (side angle side) If two sides and angle between them of one triangle is equal to the corresponding sides and angle between them of the other triangle
- ASA (angle side angle) If two angles and included side of one triangle is equal to the corresponding angle and included side of the other triangle
- SSS (side side side) If three sides of one triangle is equal to the corresponding sides of the other triangle
- RHS (right angle – hypotenuse side ) If the hypotenuse and other side of one triangle is equal to hypotenuse and the corresponding side of the other triangle
Similar triangles Two triangles are said to be similar if they have same shape but their size can be different i.e. their corresponding sides are in proportion and their corresponding angles are equal
If ΔABC is similar to ΔDEF we written this as ΔABC∼ΔDEF
A/B D/E = B/C E/F = AC/DF
- Every triangle is similar to itself
- If ΔABC∼ΔDEF then area ΔABC/area ΔDEF = (AB/DE)2= (BC/EF)2 = (AC/DF)2
Quadrilaterals A plane figure bounded by 4 line segments is called quadrilateral
Sum of all the angles of a quadrilateral is 360°
AC and BD are the diagonals of a quadrilateral
Types of quadrilateral
Parallelogram A quadrilateral whose opposite sides are parallel is called a parallelogram
- Opposite sides of a parallelogram are equal
- Opposite angles of a parallelogram are equal
- Diagonals of a parallelogram bisect each other
- Sum of consecutive angles of a parallelogram is 180°
Rectangle A quadrilateral whose opposite sides are parallel and interior angles is equal to 90°
- Opposite sides of a rectangle are equal
- All the angles of a rectangle are equal to 90°
- Diagonals of a rectangle are equal and bisect each other
Rhombus A parallelogram whose all sides are equal is called a rhombus
- Diagonals bisects each other at 90°
- Sum of the squares of the side is equal to the squares of the diagonals
Square A parallelogram whose all sides are equal and interior angles are equal to 90°
- Diagonals of a square bisect each other at 90°
- Diagonals of a square are equal
Polygons A polygon is a plane figure bounded by n straight lines
Example triangle, quadrilateral
Number of sides polygon
Regular polygons If all sides and all angles of a polygon are equal, then it is called a regular polygon
Properties of a polygon
- Sum of all interior angles of a polygon of sides n is (n – 2) × 180°
- Each exterior angle of a regular polygon of n sides is (360/n)°
- Each interior angle of a regular polygon is (n – 2) × 180°/n
- number of diagonals of a polygon of n sides is n × (n – 3)/2
- Sum of all exterior angle of a regular polygon is 360°
Circle A circle is the set of all points in a plane which are equidistant from the fixed point
This fixed point is called the center of the circle and the distance of the centre to the circle is called radius
In the above figure O is the center of circle
OD is the radius of a circle
Chord The line segment joining the two points on a circle is called a chord. In the above figure AB is the chord and CD is also a chord
Diameter the chord passing through the center is called a diameter. CD is a diameter
Tangent A line segment which touch the circle at only one point is called a tangent. EF is a tangent in the above figure
Secant A line which intersect the circle at two points is called a secant. GH is a secant in the above figure
Some important results on circle
- The perpendicular from the center of a circle to a chord bisects the chord.
- The line joining the center of circle to the mid_ point of the chord is perpendicular to the chord.
- The perpendicular bisectors of two chords of a circle intersect at the center of a circle.
- The angle subtended by an arc of the circle at the center is double the angle subtended by it at the circle.
- Chords which are equidistant from the center of a circle are equal.
- Equal chords are equidistant from the center of a circle.
- Angle in a same segment of the circle are equal.
- Tangent is perpendicular to the line joining the center of the circle to the point of contact.
- Angle in a semi_circle is 90°.
- Through a single point, an infinite number of circle can be drawn.
- Through two points , an infinite number of circles can be drawn.
- Through three-col-linear points, a unique circle can be drawn.