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

Related Topics:
Common Core (Geometry)

Common Core for Mathematics

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