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

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