How to Prepare Geometry?
Questions from Geometry in the mathematics section of the state exam are asked from following sub-topics:
- Coordinate Geometry
- Lines, Angles & their properties
- Properties of Triangles, Circles, Rectangles, Squares, Polygons etc.
Before we start, please note that we have not covered the basic properties of the above-mentioned figures.
Triangles & their properties:
Here are the must-know properties of triangles:
- The exterior angle of a triangle is equal to the sum of interior opposite angles.
- Sum of the length of 2 sides of a triangle is greater than the 3rd
- Difference between the length of 2 sides of a triangle is less than the 3rd
Circles & their properties
Here are some important properties of Circles:
- Opposite angles are supplementary in case of cyclic quadrilaterals.
- For any regular polygon, sum of all the exterior angles = 360o
- For a polygon of side n, value of each exterior angle = (360o / n)o
- For a polygon of side n, sum of all the interior angles = (n – 2) *180o
Quick Tips for Coordinate Geometry section:
- Equation of a line: ax + by + c = 0
- Slope-Intercept Equation: y = mx + c
(m = slope of the line, c = intercept on y-axis)
- Equation of line with slope ‘m’, passing through (x1, y1)
y – y1 = m (x – x1)
- Slope of a line = (y2 – y1)/ (x2 – x1) = - (coefficient of x/ coefficient of y)
- If ‘θ’ is the angle between 2 lines with slopes m1 & m2, then,
Tan θ = (m2 – m1)/ (1 + m1m2) or -(m2 – m1)/ (1 + m1m2)
Tan θ = 0, then lines are parallel,
Cot θ = 0, then lines are perpendicular.
- Two lines parallel to each other may be represented as
ax + by + c1 = 0
ax + by + c2 = 0
- Two lines perpendicular to each other may be represented as
ax + by + c1 = 0
bx - ay + c2 = 0
- Coordinates of mid-point of a line formed by points (x1, y1) & (x2, y2) is given by:
(x1 + x2)/ 2, (y1 + y2)/2
- Distance between two points, (x1, y1) & (x2, y2) is given by:
√ [(x2 – x1)2 + (y2 – y1)2]
- If points (x1, y1), (x2, y2) & (x3, y3) form a triangle, then its area is given by:
½ [x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)]
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