Geometry – Polygons and Quadrilaterals

This lesson includes:
- Quadrilaterals: Learn about rectangles, rhombi, and more!
- Regular polygons: Polygons with equal sides and angles
- Perimeter: Tricks for finding the distance around a shape
- Angles in polygons: Find a formula for the sum of the angles in any polygon
- Parallelogram angles: Opposite angles are congruent in parallelograms
- Parallelogram sides: Opposite sides are congruent in parallelograms
- Parallelogram diagonals: In parallelograms, diagonals always bisect each other
- Rectangle diagonals: Rectangles always have two congruent diagonals
- Rhombus diagonals: In rhombi, the diagonals are always perpendicular
- Trapezoid angles: Supplementary pairs of angles in trapezoids

Quadrilaterals are polygons with exactly 4 sides.

Rectangle is a quadrilateral whose angles are all right angles.

Square is a rectangle whose sides all have the same length.

Trapezoid is a quadrilateral where at least one pair of opposite sides are parallel.

Trapezoids have pairs of supplementary angles between their parallel sides.

Parallelogram is a quadrilateral where both pairs of opposite sides are parallel.

Rhombus is a quadrilateral whose sides all have the same length.

Regular polygon, every side has the same length and every angle has the same measure. 

Perimeter is the total length around a shape.

The angles in every quadrilateral add up to 360 degrees, a quadrilateral can be divided up into 2 triangles, and each triangle has 180 degrees.

Pentagons has 5 sides which add up to 540 degrees, and can be divided up into 3 triangles.

If a polygon has N sides, then every N-gon can be divided up into N – 2 triangles, the sum of its angles is (N-2) * 180 degrees.

In every rectangle, the two diagonals have the same length.

If a parallelogram’s diagonals have the same length, then it’s definitely a rectangle.

In every parallelogram, the two diagonals bisect each other. 

In every rectangle, the diagonals make four isosceles triangles.

Parallelogram angles, opposite angles are congruent in parallelograms

Angle-Angle-Side Postulate (AAS), if triangles have matching angle-angle-side, then they must be congruent.

Side-Angle-Side Postulate (SAS), if triangles have matching side-angle-side, then they must be congruent.

Angle-Side-Angle Postulate (ASA), if triangles have matching angle-side-angle, then they must be congruent.

Side-side-side postulate (SSS), If triangles have three matching side lengths, then they must be congruent.

Geometry – Polygons and quadrilaterals– Quadrilaterals | Regular polygons | Perimeter: 

Geometry – Polygons and quadrilaterals– Angles in polygons | Parallelogram angles: 

Geometry – Polygons and quadrilaterals– Parallelogram sides | Parallelogram diagonals | Rectangle diagonals: 

Geometry – Polygons and quadrilaterals– Rhombus diagonals | Trapezoid angles: