Make a table of different types of quadrilaterals and its properties
Answers
Quadrilateral shapes and their properties
There are two properties of quadrilaterals: A quadrilateral should be closed shape with 4 sides. All the internal angles of a quadrilateral sum up to 360°
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A parallelogram has four properties:
Opposite angles are equal.
Opposite sides are equal and parallel.
Diagonals bisect each other.
Sum of any two adjacent angles is 180°
Answer:
Year 10 Interactive Maths - Second Edition
Quadrilaterals
A quadrilateral is a closed plane figure bounded by four line segments. For example, the figure ABCD shown here is a quadrilateral.
Quadrilateral ABCD has two diagonals in AC and BD.
A line segment drawn from one vertex of a quadrilateral to the opposite vertex is called a diagonal of the quadrilateral. For example, AC is a diagonal of quadrilateral ABCD, and so is BD.
Types of Quadrilaterals and their Properties
There are six basic types of quadrilaterals:
1. Rectangle
Opposite sides are parallel and equal.
All angles are 90º.
The diagonals bisect each other.
A rectangle.
2. Square
Opposite sides are parallel and all sides are equal.
All angles are 90º.
Diagonals bisect each other at right angles.
A square.
3. Parallelogram
Opposite sides are parallel and equal.
Opposite angles are equal.
Diagonals bisect each other.
A parallelogram.
4. Rhombus
All sides are equal and opposite sides are parallel.
Opposite angles are equal.
The diagonals bisect each other at right angles.
A rhombus.
5. Trapezium
A trapezium has one pair of opposite sides parallel.
A regular trapezium has non-parallel sides equal and its base angles are equal, as shown in the following diagram.
A trapezium.
6. Kite
Two pairs of adjacent sides are equal.
One pair of opposite angles is equal.
Diagonals intersect at right angles.
The longest diagonal bisects the shortest diagonal into two equal parts.
A kite.
Theorem 3
Prove that the angle sum of a quadrilateral is equal to 360º.
Proof:
A diagonal AC divides the quadrilateral ABCD into two triangles. q and v are two angles in triangle ACD and p and u are two angles in ABC.
In triangle ABC, p + u + B = 180 degrees {Angle sum of triangle} ...(1). In triangle ACD, q + v + D = 180 degrees {Angle sum of triangle} ...(2). Adding (1) and (2) gives (p + q) + (u + v) + B + D = 360 degrees so we find A + B + C + D = 360 degrees.
Hence the angle sum of a quadrilateral is 360º.