As the name suggest, a triangle is a polygon having three sides and three angles. The sum of interior angle of a triangle to be equal to \(180^{\circ}\)

**Similarity of Triangle-**

Two triangles are similar, if

**(i) **their corresponding angles are equal and

**(ii) **their corresponding sides are in the same ratio (or proportion).

**Pythagoras Theorem- **

**In a right-angled triangle the sum of squares of two sides is equal to the square of the hypotenuse of the triangle.**

**Proof of Pythagoras Theorem-**

Consider a right triangle, right angled at B.

From Pythagoras Theorem, we have

\(AC^{2} = AB^{2} + BC^{2}\)

**Construction- **

Draw \(BD \perp AC\)

Now, \(\bigtriangleup ADC \sim \bigtriangleup ABC\)

So, \(\frac{AD}{AB} = \frac{AB}{AC}\)

or, \(AD. AC = AB^{2}\)

Also, \(\bigtriangleup BCDC \sim \bigtriangleup ABC\)

So, \(\frac{CD}{BC} = \frac{BC}{AC}\)

or, \(CD. AC = BC^{2}\)

Adding (i) and (ii),

\(AD. AC + CD. AC = AB^{2} + BC^{2}\)

\(AC(AD + DC) = AB^{2} + BC^{2}\)

\(AC(AC) = AB^{2} + BC^{2}\)

\(\Rightarrow AC^{2} = AB^{2} + BC^{2}\)

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