Triangle is a basic polygon which has three vertices and three edges(sides).

Three non-collinear points develop a triangle.

Type of Triangles (based on side)

(i) Scalene triangle: (The length of three sides are unequal).

(ii) Equilateral Triangle: (The length of all three sides are equal) and each angle will be 60⁰.

(iii) Isosceles Triangle: (In isosceles triangle any two sides will be equal).

Type of Triangles (based on angle)

(i) Right Triangle:In right triangle one angle will be equal to 90⁰.

(ii) Acute Triangle: In acute triangle all angle will be less than 90⁰.(angle less than 90⁰ is known as acute angle).

(iii) Obtuse Triangle: In obtuse triangle one angle will be more than 90⁰(angle more than 90⁰ is known as obtuse angle).

(iv) Isosceles Right Triangle: In this triangle any one angle will be equal to 90⁰ and any two sides will be equal.

Formula to calculate area of triangle.

(i) Heron's formula: This formula is applicable when length of all three sides are given(one can't find height easily)
area of triangle =

(ii) Area of Triangle =

This formula is applicable when height of the triangle (altitude) is given or triangle is right angled triangle (one angle is 90⁰).

(iii) Area of Triangle =

This formula is applicable when coordinates of vertices of a triangle are given.This formula can also be written in determinant form.

Important Points

1 . The sum of the all three angles of a triangle is 180° .



where the sum of angle 1,2 and 3 is 180°

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2 . Exterior Angles Theorem : if a side of a triangle is produced , the Exterior angle formed in this case will be equal to the sum of the two interior opposite angle .



where ∠ 1 is exterior angle ∠3 , ∠4 and ∠2 are interior angles as per this property

∠ 1 = ∠ 3 + ∠ 4

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3 . If a line divides any two sides of a triangle in the same ratio , then the line is parallel to the third side of the triangle

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4 . The line joining the mid-points of two sides of a triangle is parallel to the third side

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5 . Thales Theorem or Basic Proportionality Theorem : If a line drawn parallel to one side of a triangle intersecting the other two side then it divides the two sides in the same ratio .

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6 . Two triangles are called similar triangle if corresponding angles are equal and corresponding sides are Proportional .

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7 . The ratio of areas of two similar triangles is equal to the ratio of

(a) . The squares of any two corresponding sides

(b) The squares of the corresponding altitudes

(c) . The squares of corresponding medians

(d) . The square of the corresponding angle bisector segment

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8 . Three times the sum of the square of the sides of a triangle is equal to four times the sum of the squares of the medians of the triangles .

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9 . Three times the square of any side of an Equilateral triangle is equal to four times the square of the altitude.