PYTHAGORAS THEOREM

The Pythagoras theorem helps to find the side of the triangle. This is possible only for Right angled triangles and the important note is that every triangle can be splitted into two right angle triangles

1. PYTHAGORAS THEOREM Your best friend to solve Right-angled triangles. Presented by Vaishika G

2. Overview Pythagoras Theorem (also called Pythagorean Theorem)  is an important topic in Mathematics, which explains the relation between the sides of a  right-angled triangle . Pythagoras theorem is basically used to find the length of an unknown side and the angle of a triangle. By this theorem, we can derive the base, perpendicular and hypotenuse formulas. The sides of the right triangle are also called Pythagorean triples.

3. Right – Angled TriaNgle A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees. The sides that include the right angle are perpendicular and the base of the triangle. The third side is called the hypotenuse, which is the longest side of all three sides.

4. Statement Pythagoras theorem states that “ In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides “.

5. Formula Consider the triangle given in the previous slide: Where “a” is the perpendicular, “b” is the base, “c” is the hypotenuse. According to the definition, the Pythagoras Theorem formula is given as:  

6. Proof Given: A right-angled triangle ABC, right-angled at B. To Prove : AC 2  = AB 2  + BC 2 Construction: Draw a perpendicular BD meeting AC at D.

7. Proof We know, △ADB ~ △ABC Therefore, (corresponding sides of similar triangles) Or, AB 2  = AD × AC ……………………………..……..(1) Also, △BDC ~△ABC Therefore,  

8. Proof Or, BC 2 = CD × AC ……………………………………..(2) Adding the equations (1) and (2) we get, AB 2  + BC 2  = AD × AC + CD × AC AB 2  + BC 2  = AC (AD + CD) Since, AD + CD = AC Therefore, AC 2  = AB 2  + BC 2 Hence, the Pythagorean theorem is proved.

9. Application To know if the triangle is a right-angled triangle or not. In a right-angled triangle, we can calculate the length of any side if the other two sides are given. To find the diagonal of a square.

10. Wrapping it up The Pythagorean Theorem can be used only on _____triangles. When should the Pythagorean Theorem be used? What should be done first when solving a word problem involving the Pythagorean Theorem? What must be done before writing the answer to a Pythagorean Theorem problem? Right When the length of 2 sides are known and the length of 3rd side is needed Draw and label triangle Check to see whether the answer should be rounded or not