One of the hardest sections to crack without preparation and one of the easiest with preparation. With so many formulas to learn and remember, this section is going to take a lot of time to master. Remember, read a formula, try to visualize the formula and solve as many questions related to the formula as you can. Knowing a formula and knowing when to apply it are two different abilities. The first will come through reading the formulae list and theory but the latter can come only through solving many different problems.
Basic Formulae:
Consider parallel lines AB, CD and EF as shown in the figure.
XY and MN are known as transversals
$$\angle $$ XPQ = $$\angle $$ PRS = $$\angle $$ RTU as corresponding angles are equal
Interior angles on the side of the transversal are supplementary. i.e. $$\angle $$ PQS + $$\angle $$ QSR = 180 degrees
Exterior angles on the same side of the transversal are supplementary. i.e. $$\angle $$ MQB + $$\angle $$ DSU = 180 degrees.
Two transversals are cut by three parallel lines in the same ratio i.e. PR / RT = QS / SU
An angle less than 90 degree is called an acute angle. An angle greater than 90 degrees is called an obtuse angle.
Nomenclature
A line joining the mid point of a side with the opposite vertex is called a median.* A perpendicular drawn from a vertex to the opposite side is called the altitude
The point of intersection of the three medians is the centroid
A triangle with two sides equal is called an isosceles triangle. A triangle with all sides equal is called an equilateral triangle. The two angles of an isosceles triangle that are not contained between the equal sides are equal. All angles of an equilateral triangle equal 60 degrees.
Important Points to Remember:
Circle Properties
Angle subtended by a chord on the circumference is half of the angle subtended by the same chord on the centre.
Surface area of different solids:
Area of a triangle A
Area of a quadrilateral
Volume of different solids:
Apollonius theorem states that in a triangle ABC, if AD is a median to BC then $$AB^2+AC^2=2\cdot\left(AD^2+BD^2\right)$$
Apollonius theorem
In a triangle ABC, if AD is the median to side BC then by Apollonius theorem, $$2*(AD^2+BD^2)$$ = $$AC^2$$ + $$AB^2$$.