Prove that the sum of angles of a quadrilateral is 360.
To prove that the sum of angles of a quadrilateral is 360 degrees, we can use the fact that the sum of angles in a triangle is 180 degrees.
Here's how we can proceed:
1. Start with a quadrilateral ABCD.
2. Draw a diagonal from one vertex to another. For example, draw a diagonal from A to C.
3. By doing this, we have divided the quadrilateral into two triangles, such as triangle ABC and triangle ADC.
4. Since the sum of angles in each triangle is 180 degrees, the sum of angles in triangle ABC is 180 degrees and the sum of angles in triangle ADC is also 180 degrees.
5. Therefore, the sum of angles in the quadrilateral ABCD is equal to twice the sum of angles in one of the triangles, which is 2 * 180 degrees = 360 degrees.
Hence, we have proved that the sum of angles in a quadrilateral is indeed 360 degrees.
I assume you have seen the proof that the sum of angles of a triangle is 180°
If not you can find may using google.
Now, divide the quadrilateral into two triangles. Done.
In fact, extending the idea makes it easy to prove that the interior angles of an n-gon add up to
(n-2)*180°