Help on how many triangles

Introduction to how many triangles are there:
In math, the triangles are closed figure with three sides. The triangles has different types and each has different size of angles. If we add the angles of triangles, we get the answer as 180 degree. We can count how many triangles are present in some pictures by using formula.Here we can see about how many triangles are there with examples.

Explanation for How many Triangles.

The formula for finding how many triangles are there in pictures:

Step 1: We can add the consecutive odd numbers and get the answer equal to N². That is 1 + 3 + 5 + …. + (2N -1) = N².

Step 2: Using induction, we show the elementary proof and assume N = k. This will also help us on blank unit circle.

Therefore, 1 + 3 + 5 + …+ (2k – 1) = k².

Step 3: Let take N = k + 1.

That is 1 + 3 + 5 +….+( 2k – 1) + [2 (k + 1) – 1] = (k + 1)².

Step 4: Compare the left side of step 3 and step 4 equation.

Get the answer as [ 2(k + 1) – 1] = 2k + 1.

Step 5: The right hand sides are (k + 1)² – k² = 2k + 1.

This is denote induction proof