## Wednesday, August 26, 2015

### Basics of Polygons(Convex and Concave),Interior and Exterior Angles,Number of Diagonals and Triangles in a Polygon

In this video I have first completed the explanation of those questions relating to triangles which I was not able to finish in my previous video. The questions are listed below

Question 6. In triangle ABC, if E divides AB in the ratio 3:1 and F divides BC in the ratio 3:2, find the ratio of the areas of triangle BEF and ABC.

Question 7. D is the midpoint of side BC of triangle ABC. DP bisects angle ADB meeting AB at P, and DQ bisects angle ADC meeting AC at Q. Prove that PQ is parallel to BC

Question 8. X is the centroid of triangle ABC with height being h units. If a line DE parallel to BC, cuts the triangle ABC at a height of h/4 from BC, find the distance XM in terms of AX if M  is the centroid of triangle ADE.

Question 9. In a triangle XYZ, the bisectors of angle X meet YZ at A. A straight line parallel to YZ meets XY, XA and XZ at B,C,D the prove the below equations -

(a) XY.AZ = XZ.YA
(b) XB.CD = XD.BC

After that I have explained the basics of Polygons. I have told the types of polygons - Convex Polygon and Concave Polygon, I have explained what interior and exterior angles are and how their formulas are derived. The sum of all exterior angles of a convex polygon is 360 degrees - the proof of this has been detailed in the video. Also the sum of all interior angles of a convex polygon is (n-2)180 degree - the proof of this formula has also been explained by me.

After that I have explained the formula of how to find the number of diagonals in any convex polygon and also the proof of the formula and relating to it I have explained how many triangles are there in a convex polygon. After this in my next video I will carry on with a detailed analysis of convex quadrilaterals.

Happy to listen your doubts, experience and criticism in the comment section below.