**Right angled Triangle:-**

##### A triangle in which one of the angles measures 90 ^{0 }is called a right angled triangle or simply right triangle.

##### observe figure ABC is a right angle triangle at Angle B opposite side of right angle is biggest side AC is the longest side, it is called “hypotenuse”.

**In a right triangle, the square ****of length of the hypotenuse is ****equal to the sum **** of the squares of lengths **** of the other two sides. **

**Given :**

**ABC ****is ****a right triangle, right angle at B**

**RTP **: AC ^{2} = AB^{2} + BC^{2}

**Construction **: Draw BD perpendicular to AC.

**Proof **:

**In ∆ ****ADB ****and ∆****ABC**

**∠****A= ∠A**

*∠**ADB=*** ***∠**ABC***= **90 ^{0}

*∠*

*ADB=*

*∠*

*ABC*

**By AA similarity property**

*∆ADB***~ ***∆ABC*

*∆ADB*

*∆ABC*

#### sides are proportional

**Similarly in ****∆ ****BDC**** ****and ****∆****ABC**

*∠**C=*** ***∠**C*

*∠*

*C=*

*∠*

*C*

*∠**BDC=*** ***∠**ABC***= 90 **^{0}

*∠*

*BDC=*

*∠*

*ABC*

^{0}

**By AA similarity property**

*∆BDC*** ~ ***∆ABC*

*∆BDC*

*∆ABC*