Reading 18: Geometry Review

Citation

Handout distributed in class.

Summary

The handout distributed in class contains some basics of geometry. It starts with the introduction of Pythagoras theorem which states in a  right angle triangle the hypotenuse squared is equal to base squared plus height squared. If the angle between the base and hypotenuse is theta then the length of the base is hCos(theta) and length of the height is equal to hSin(theta) where h is the length of the hypotenuse.

Also, relationship between the sides of a triangle is discussed:

Also relation relation between sides of a parallelogram and its area are discussed. The area of a parallelogram with diagonally opposite endpoints as (ax, ay) and (bx, by) is determinant of the matrix [ax, bx; ay, by]

Discussion

To prove that area of a parallelogram is equal to the determinant of the matrix made by the coordinates of the diagonally opposite points, you first divide the parallelogram into two equal triangles divided by the diagonal. Then calculate the area of each triangle using formulas discussed previously. Then add those two areas to get the final area which comes out to be ax*by - ay*bx which is the determinant of the matrix [ax, bx; ay, by]