Properties of Polygons

A series of free, online High School Geometry Video Lessons.
Videos, worksheets, and activities to help Geometry students.

In this lesson, we will learn

  • the properties of a parallelogram
  • how to solve a problem with trapezoidal arches
  • the properties of a rhombus
  • the properties of a rectangle and a square



Parallelogram Properties

Properties of parallelograms often show up in geometric proofs and problems. Parallelogram properties apply to rectangles, rhombi and squares. In a parallelogram, opposite sides are congruent, opposite angles are congruent, consecutive angles are supplementary and diagonals bisect each other. Other important polygon properties to know are trapezoid properties, and kite properties.

How to identify all of the special properties of parallelograms and use them to solve problems.

This video discusses the definition of a parallelogram and the properties of parallelograms. It gives seven properties in detail so you have a full understanding of each property that a parallelogram has.



Trapezoid Arch and Panel Design Problem

When identifying missing angle measurements in trapezoid design and trapezoidal arc problems, knowledge of trapezoid and angle properties is necessary. In a trapezoid design problem, one part of a shape is given while the rest of the shape needs to be imagined. With knowledge of missing angles, it is possible to find the vertex and the other angles by knowing about trapezoid properties and corresponding angles.

How to strategize about solving a problem with trapezoidal arches.



Rhombus Properties

Properties of rhombi often show up in geometric proofs and many other types of problems. All parallelogram properties apply to rhombus properties since a rhombus is a type of parallelogram. In a rhombus, there are (1) two pairs of parallel sides, (2) four sides that are all congruent to each other, (3) diagonals that bisect the angles, and (4) diagonals that are perpendicular bisectors of each other.

How to define a rhombus and compare it to a square and rectangle.

Properties of Rhombi (Rhombus)

Thid video discusses all 10 properties of rhombi. It explains what properties differentiate a rhombus from a parallelogram. It also goes over 2 example problems dealing with interior angles, side length, and diagonals.



Rectangle and Square Properties

Squares and rectangles are special types of parallelograms with special properties. A square is a type of equiangular parallelogram and square properties include congruent diagonals and diagonals that bisect each other. A rectangle is a type of regular quadrilateral. Rectangle properties include (1) diagonals that are congruent, (2) perpendicular diagonals that bisect each other and (3) diagonals that bisect each of the angles.

How to define a rectangle and a square.

Special Properties of rectangle, rhombus and square




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