Quadrilaterals

Quadrilaterals

​Dr. Tom Giles

Polygons with four sides

Parallelograms

​Since Quadrilaterals are polygons with four sides, Parallelograms are Special Quadrilaterals

Parallelograms
(& Special Parallograms)

Parallelograms have...

• Opposite Sides that are Parallel

• Opposite Sides that are Congruent

• Opposite Angles that are Congruent

• Consecutive Angles that are Supplementary

• Diagonals that bisect each other

Parallelograms have...

• Opposite Sides that are Parallel

• Opposite Sides that are Congruent

• Opposite Angles that are Congruent

• Consecutive Angles that are Supplementary

• Diagonals that bisect each other

Rectangles have...

• Opposite Sides that are Parallel

• Opposite Sides that are Congruent

• Opposite Angles that are Congruent

• Consecutive Angles that are Supplementary

• Diagonals that bisect each other

​All four angles are right angles Diagonals are congruent

​Plus:

Rhombuses have...

• Opposite Sides that are Parallel

• Opposite Sides that are Congruent

• Opposite Angles that are Congruent

• Consecutive Angles that are Supplementary

• Diagonals that bisect each other

​All four sides are congruent
Diagonals are perpendicular
Diagonals bisect opposite angles

​Plus:

Squares have...

• Opposite Sides that are Parallel

• Opposite Sides that are Congruent

• Opposite Angles that are Congruent

• Consecutive Angles that are Supplementary

• Diagonals that bisect each other

Four congruent sides​
Four right angles
Diagonals are perpendicular
Diagonals bisect opposite angles

​Plus:

So a square is a rhombus and a rectangle and a parallelogram and a quadrilateral.

Some text here about the topic of discussion

Poll

A parallelogram with four right angles is a

• rhombus

• rectangle

• square

Poll

A parallelogram with four congruent sides is a

• rhombus

• square

• rectangle

Poll

A parallelogram with four congruent sides and four right angles is a

• rhombus

• rectangle

• square

Objectives

• To define and classify special types of parallelograms

• To use properties of diagonals of rhombi and rectangles​

Open Ended

Determine the values of the Rectangle shown at the left.

Open Ended

Determine the values of the Rectangle shown at the left.

Open Ended

Determine the values of the Rhombus shown at the left.

Open Ended

Determine the values of the Square shown at the left.

Identifying Trapezoids

Parallelogram Definition...



A Parallelogram is a Quadrilateral with Two Pairs of Parallel sides.

Multiple Choice

• yes

• no

Multiple Choice

• yes

• no

Multiple Choice

• yes

• no

Multiple Choice

• yes

• no

Multiple Choice

• A

• B

• C

• D

Identifying Kites

Kites

A kite is a quadrilateral with two pairs of consecutive sides congruent and no opposite sides congruent.

Kites

In geometry, "vertical angles" refer to the angle formed by two lines that meet at a common point, called the vertex; essentially, it's the angle associated with a specific vertex where two sides of a shape intersect.

Kites

In geometry, "vertical angles" refer to the angle formed by two lines that meet at a common point, called the vertex; essentially, it's the angle associated with a specific vertex where two sides of a shape intersect.

In geometry, "non-vertical angles" refer to the angles in a kite that are NOT located between two pairs of congruent sides, essentially the angles that are opposite the vertex angles, which are always congruent to each other in a kite.

Draw

Find the measure of angle V.

Draw

Find the measure of angle W.

Draw

Find the measure of angle G.

Draw

Find the measure of angle G.

Draw

Find the measure of angle x.

Draw

Find the measure of angle y.