# Prove Parallelogram Theorems

Videos and lessons to help High School students learn how to prove theorems about parallelograms.

Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

Common Core: HSG-CO.C.11

Proof - Opposite Sides of Parallelogram Congruent
Proving that a figure is a parallelogram if and only if opposite sides are congruent.

Proof - Opposite Angles of Parallelogram Congruent
Showing that opposite angles of a parallelogram are congruent.

Proof - Diagonals of a Parallelogram Bisect Each Other
Proving that a quadrilateral is a parallelogram if and only if its diagonals bisect each other.

Proving Quadrilaterals are Parallelograms
Congruent and Parallel Opposite Sides Theorem: If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.
If the diagonals of a quadrilateral bisects each other, then the quadrilateral is a parallelogram.

Converses of the Parallelogram Theorems
If both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogram.
If the angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram.
If both pairs of opposite angles in a quadrilateral are congruent, then the quadrilateral is a parallelogram
Find values that determine a parallelogram.

Proving a Quadrilateral a Parallelogram
This video geometry lesson gives the prove of two parallelogram theorems.
The first is: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
The second is: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
It uses the theorems: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram and If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram to solve problems.

Rectangles are parallelograms with congruent diagonals theorem
If a parallelogram has congruent diagonals, then it is a rectangle.

Special Parallelograms: Rhombus, Rectangles
This video lesson discusses the properties of the special parallelograms: rectangle and rhombus.
Proof that each diagonal of a rhombus bisects two angles of the rhombus.
The first example models how to find the measures of a rhombus when given one measure. Example 2 models using the property of rectangles that states: The diagonals of a rectangle are congruent. Examples 3 and 4 require higher order thinking and a written explanation.

Discovering the Properties of Quadrilaterals
Grades 9-12 / Math / Geometry
CCSS: Math.G.CO.10 Math.G.CO.11 Math.G.CO.12
Lesson Objective
Form conjectures to discover the properties of quadrilaterals

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.