Types of Quadrilaterals
Identifying Geometric Shapes by their properties
Parallelogram
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Opposite angles in a parallelogram are equal
Opposite sides in a parallelogram are parallel Opposite sides in a parallelogram are equal
|
Rectangle
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Opposite sides in a rectangle are parallel
Opposite sides in a rectangle are equal Angles in a rectangle are equal to 90°
|
Square
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All angles in a square are equal to 90°
All sides of a square are equal Opposite sides in a square are parallel
|
RHombus
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Opposite sides in a rhombus are parallel
Opposite angles of a rhombus are equal All sides of a rhombus are equal
|
Trapezium
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1 pair of opposite parallel sides |
Kite
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2 pairs of equal adjacent sides
1 pair of opposite equal angles
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Now that you know about 6 different types of quadrilaterals. Move the points (vertices) around and see how many different quadrilaterals you can find in the interactive below. (Watch this video if you would like to see this interactive in action -)
Worked Examples
Question 1
For each of the shapes below, choose the most precise classification.
A quadrilateral is illustrated whose two opposite sides are congruent indicated by the same hash marks on the sides and its sides are perpendicular to each other indicated by small squares on all four corners. Trapezium
ARectangle
BSquare
C
A quadrilateral is illustrated whose all four sides are congruent indicated by the same hash marks on the sides and are perpendicular to each other indicated by small squares on all four corners. Square
ATrapezium
BRectangle
C
A quadrilateral is illustrated whose opposite horizontal sides are parallel indicated by the same arrowmarks on the sides. Its right side is perpendicular to the two opposite horizontal sides of the quadrilateral as indicated by the small squares in two right corners. Its top base is longer than the bottom base. Trapezium
ARectangle
BSquare
C
A quadrilateral is illustrated whose opposite sides are congruent indicated by the same hash marks on the sides, and all four sides are perpendicular to each other indicated by small squares on all four corners. Trapezium
ARectangle
BSquare
C
A quadrilateral is illustrated whose opposite horizontal sides are parralel indicated by the same arrowhead marks on the sides. The top base is longer than the bottom base. None of the sides are perpendicular to each other. Trapezium
ASquare
BRectangle
C
Question 2
Patricia draws a quadrilateral, and covers it up. She tells Glen that the quadrilateral consists of right angles only. From this information, Glen knows that the quadrilateral is definitely a:
Rhombus
ASquare
BTrapezium
CRectangle
D
Solving problems
When solving angle problems in geometry one of the most important components is the reasoning (or rules) you use to solve the problem. You will mostly be required in geometry problems to not only complete the mathematics associated with calculating angle or side lengths but also to state the reasons you have used. Read through each of these rules and see if you can describe why and draw a picture to represent it.
Properties of quadrilaterals
Parallelogram
- Opposite sides in a parallelogram are parallel
- Opposite angles in a parallelogram are equal
- Opposite sides in a parallelogram are equal
Rectangle
- Opposite sides in a rectangle are parallel
- Opposite sides in a rectangle are equal
Square
- All sides of a square are equal
- Opposite sides in a square are parallel
Rhombus
- Opposite sides in a rhombus are parallel
- Opposite angles of a rhombus are equal
- All sides of a rhombus are equal
Trapezium
- An isosceles trapezium (trapezoid) has 2 pairs of adjacent angles equal
- A trapezium (trapezoid) has one pair of opposite sides parallel
- An isosceles trapezium (trapezoid) has one pair of opposites sides equal
Kite
- A kite has 2 pairs of adjacent sides equal
- A kite has 1 pair of opposite angles equal
A summary of the geometrical properties of angles can be found here.
A summary of the geometrical properties of triangles can be found here.