Properties of parallelograms

Learning Objectives Identify the five key properties of parallelograms. Apply the properties of parallelograms to find unknown side lengths and angle measures. Use the properties of diagonals to solve for unknown values in a parallelogram. Set up and solve algebraic equations based on the geometric properties of parallelograms. Use coordinate geometry formulas (slope, distance) to verify that a given quadrilateral is a parallelogram. Construct a basic two-column proof involving properties of parallelograms. Have you ever noticed the pattern on a chain-link fence or the structure of a folding scissor lift? 🧐 You're looking at parallelograms in action! This tutorial will explore the fundamental properties that define a parallelogram, a special type of quadrilateral. Und...

TermDefinitionExample ParallelogramA quadrilateral with two pairs of parallel opposite sides.In quadrilateral ABCD, if side AB is parallel to side DC and side AD is parallel to side BC, then ABCD is a parallelogram. Opposite SidesIn a quadrilateral, sides that do not share a common vertex (corner).In parallelogram ABCD, AB and DC are opposite sides. AD and BC are also opposite sides. Opposite AnglesIn a quadrilateral, angles that do not share a common side.In parallelogram ABCD, ∠A and ∠C are opposite angles. ∠B and ∠D are also opposite angles. Consecutive AnglesAngles in a polygon that share a common side.In parallelogram ABCD, ∠A and ∠B are consecutive angles because they share side AB. Similarly, ∠B and ∠C are consecutive. DiagonalA line segment that connects two non-consecutive vertic...

Opposite Sides Property In a parallelogram, opposite sides are congruent. If ABCD is a parallelogram, then \( \overline{AB} \cong \overline{DC} \) and \( \overline{AD} \cong \overline{BC} \). Use this rule to find the length of a side when you know the length of its opposite side, or to set up an equation if the side lengths are given as algebraic expressions. Opposite Angles Property In a parallelogram, opposite angles are congruent. If ABCD is a parallelogram, then \( \angle A \cong \angle C \) and \( \angle B \cong \angle D \). Use this rule to find the measure of an angle when you know the measure of its opposite angle. This is also useful for setting up algebraic equations. Consecutive Angles Property In a parallelogram, consecutive angles are supplementary. For e...