Unit-I: Sets and Functions
Unit-II: Algebra
Unit-III: Coordinate Geometry
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability

Some important Properties

(i) The area of any triangle is equal to four times the area of the triangle formed by joining the midpoints of its sides.

In the above figure   4 \times \text { area of } \triangle PQR =\text { area of } \triangle ABC

(ii) The diagonals of a rhombus bisects at right angles.

 m < POQ = 90 ^o

(iii) The internal bisectors of angles of a triangle are concurrent.

Here  'I' is called incentre.

(iv) The line segment joining the midpoints of two sides of a triangle is a parallel to the third and half of its length.

 \overline{PQ} \parallel \overline{BC} \text { and} PQ = \dfrac{1}{2} BC

(v) The altitude of a triangle are concurrent.

Here  'H' is the orthocenter

(vi) Medians of a triangle are concurrent.

Here  'G'  is the centroid

(vii) The perpendicular bisectors of the sides of a triangle are concurrent .

Here ' O' is the Circumference

(viii) An angle in a semicircle is a right angle.

 m < ACB =90^o

Note:

Euler Line:

The orthocenter  (H) , Centroid  ( G )  and the circumcenter  ( O )   of a non-equilateral triangle are collinear and the aligned line is called Euler line.

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