AB and CD are parallel lines in the picture.
Prove that AP .PC=BP. PD

In the figure. below, the lines A B and CD are parallel and M is the mid point of A B . i) Compute the angles of Delta AMD, triangle MBC and Delta DCM? ii) What is special about the quadrilaterals AMCD and MBCD?

In the quadrilateral ABCD,AB and CD are parallel. angleA+angleC=190^o If AD=BC , then prove that a circle an be drawn through the points A,B,C and D. .

P is a point inside the rectangle ABCD Prove that PA^2+ PC^2= PB^2 +PD^2 : .

In the picture below, the top vertex of a triangle is joined to the midpoint of the opposite side and then the point dividing this line in the ratio 2:1 is joined to the other two vertices. Prove that the areas of all three triangles in the picture on the right are equal to a third of the area of the whole triangle

In the picture below, the top vertex of a triangle is joined to the midpont of the opposite side and then the point dividing this line in the ratio 2:1 is joined to the other two vertices: Prove that the areas of all three triangles in the picture on the are equal to a third of the area of the whole triangle.

In the picture below, the side AC of the triangle ABC is extended by D, by adding the length of the side CB. Then the line through C parallel to DB is drawn to meet AB at E. Prove that CE bisects angle C

In the figure AB is a chord and CD is the diameter perpendicular to it. Prove that ABC is, an Isosceles triangle.

In the figure, O is the center of the circle and A B and CD are chords with AB=CD Prove that angle < OAB=< OCD