**Triangles**

**Triangle **

Contents

__Triangles__

- Surveyor use it to find height of building
- It is used in construction of Bridge
- It is also used to build roof of the house
- Some Street sign broads are triangular
- It is used in Astronomy
- Also used in Carpentry & many other fields.

__Congruent Figures__

- their corresponding angles are equal and
- Their corresponding sides are in the same ratio (or proportion).

__Similarity of Triangles__

- their corresponding angles are equal
**Or** - Their corresponding sides are in the same ratio (or proportion).

**Thales theorem:**The ratio of any two corresponding sides in two equiangular triangles is always the same.

**Theorem 1 :**If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

**Converse Theorem 2**: If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

__Criteria for Similarity of Triangles__

- their corresponding angles are equal or
- their corresponding sides are in the same ratio (or proportion).

**Theorem 3:**If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar.

**Theorem 4 :**If in two triangles, sides of one triangle are proportional to (i.e., in the same ratio of ) the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similiar.

**Theorem 5 :**If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar.

__Areas of Similar Triangles__

**Theorem 6 :**The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

__Pythagoras Theorem__

**Theorem 7 :**If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse then triangles on both sides of the perpendicular are similar to the whole triangle and to each other.

**Pythagoras Theorem 8 :**In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

**Converse Pythagoras Theorem 9 : **In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

**Also Read :**

### MATHS Revision Notes

Chapter:01 Real Numbers System

Chapter:02 Polynomials

Chapter:03 Pair of Linear Equations in Two Variables

Chapter:04 Quadratic Equation

Chapter:05 Arithemetic Progressions

Chapter:06 Triangles

Chapter:07 Coordinate Geometry

Chapter:08 Introduction to Trignometry

Chapter:09 Some Application Of Trignometry

Chapter:10 Circles

Chapter:11 Constructions

Chapter:12 Area Related to Cirles

Chapter:13 Surface Area Volume

Chapter:14 Stastistics

Chapter:15 Probability