Question

Draw a convex quadrilateral ABCD, where the diagonals intersect at point M. Prove: If ABCD is a parallelogram, then M is the midpoint of each diagonal.

Answer 1

Convex quadrilaterals: In a convex quadrilateral, all interior angles are less than 180° and the two diagonals both lie inside the quadrilateral.

CYCLIC QUADRILATERAL: The four sides are tangents to an inscribed circle. A convex quadrilateral is tangential if and only if opposite sides have equal sums.

PARELLELOGRAM: One special kind of polygons is called a parallelogram. It is a quadrilateral where both pairs of opposite sides are parallel.

There are six important properties of parallelograms to know:

1. Opposite sides are congruent (AB = DC).
2. Opposite angels are congruent (D = B).
3. Consecutive angles are supplementary (A + D = 180°).
4. If one angle is right, then all angles are right.
5. The diagonals of a parallelogram bisect each other.
6. Each diagonal of a parallelogram separates it into two congruent triangles.

1. 

△ACD≅△ABC.

the four sides are tangents to an inscribed circle. A convex quadrilateral is tangential if and only if opposite sides have equal sums.