**Proving the pythagorean theorem :**

In a right triangle, the two sides that form the right angle are the legs. The side opposite the right angle is the hypotenuse.

In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

If a and b are legs and c is the hypotenuse,

a² + b² = c²

**Step 1 :**

Draw a right triangle on a piece of paper and cut it out. Make one leg shorter than the other.

**Step 2 :**

Trace your triangle onto another piece of paper four times, arranging them as shown. For each triangle, label the shorter leg a, the longer leg b, and the hypotenuse c.

**Step 3 :**

Find the area of the unshaded square.

c² square units ----- (1)

**Step 4 :**

Label the unshaded square with its area.

**Step 5 : **

Trace your original triangle onto a piece of paper four times again, arranging them as shown. Draw a line outlining a larger square that is the same size as the figure you made in step 2.

**Step 6 :**

Find the area of the unshaded square at the top right and left of the figure in step 5.

a² square units and b² square units

**Step 7 :**

Label the unshaded squares with their areas.

**Step 8 :**

Find the total area of the unshaded regions in step 5.

(a² + b²) square units -----(2)

**Step 9 :**

Because both (1) and (2) represent the total area of the unshaded region, they are equal.

So, we have

a² + b² = c²

Hence, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

1. Explain whether the figures in step 2 and step 5 have the same area.

Yes, the figures in step 2 and step 5 have the same area. Because, the outlines of the figures are the same size.

2. Explain whether the unshaded regions of the figures in step 2 and step 5 have the same area.

Yes, the shaded regions have the same area. Subtracting the area of the shaded region from the total area gives the same area for the unshaded region in each figure.

3. Write an equation relating the area of the unshaded region in step 2 and step 5 have the same area.

a² + b² = c²

After having gone through the stuff given above, we hope that the students would have understood "Proving the pythagorean theorem".

Apart from the stuff given above, if you want to know more about "Proving the pythagorean theorem", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**