BY: Group 4

TYPES OF QUADRILATERA

L AND ITS PROPERTIES

LEARNING OBJECTIVES•To understand the difference between the types of quadrilaterals.•To understand the properties of the types of special quadrilaterals.

TYPES OF QUADRILATERALS

• In this presentation we are going to learn some special quadrilaterals:

• Rectangle• Rhombus• Kite• Arrowhead• Isosceles trapezium

WHAT IS A QUADRILATERAL??

• The word “quadrilateral” comes from two Latin words “quadri” which means ‘a variant of four’ and “lateral” which means side.• Any four-sided shape is a quadrilateral.• A quadrilateral is a closed figure with four angles, four sides and four vertices

WHAT IS A QUADRILATERAL

PROPERTIES OF A QUADRILATERAL

• Interior Angle Sum Property: According to this property, the sum of the interior angles of the quadrilateral is 360°• Exterior Angle Sum Property: According to this property, the sum of the exterior angles of the quadrilateral is 360°

RECTANGLE

The rectangle, like the square, is one of the most commonly known quadrilaterals. It is defined as having all four interior angles 90° (right angles).

• It is a polygon with four sides, four vertices and four equal angles.

Properties of a rectangle

• Opposite sides are parallel and congruent• The diagonals bisect each other • The diagonals are congruent

D C

A B

RHOMBUS

• Rhombus is a 4-sided flat shape with straight sides where all sides have equal length.

• It is a type of parallelogram.

• A rhombus has all sides equal, while a rectangle has all angles equal.

• A rhombus has alternate angles equal, while a rectangle has alternate sides equal.

• A rhombus has an inscribed circle, while a rectangle has a circumcircle.

• A rhombus has an axis of symmetry through each pair of opposite vertex angles, while a rectangle has an axis of symmetry through each pair of opposite sides.

• The diagonals of a rhombus intersect at equal angles, while the diagonals of a rectangle are equal in length.

PROPERTIES OF A RHOMBUS

KITE

• A quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other is called a kite.

• A kite has 4 sides, 4 vertices and 4 angles.

• Two disjoint pairs of consecutive sides are congruent by definition • The diagonals are perpendicular.• One diagonal (segment KM, the main diagonal) is the perpendicular bisector of the other diagonal (segment JL, the cross diagonal). (The terms “main diagonal” and “cross diagonal” are made up for this example.)• The main diagonal bisects a pair of opposite angles (angle K and angle M). • The opposite angles at the endpoints of the cross diagonal are congruent (angle J and angle L).Note: Disjoint means that the two pairs are totally separate.

PROPERTIES OF A KITE

An arrowhead is a type of quadrilateral with one pair of sides with equal length

• It is also called as a concave quadrilateral.• One pair of sides with equal length.• It has no parallel sides

ARROWHEAD

ISOSCELES TRAPEZIUM

• An isosceles trapezoid is a trapezoid where the legs have equal length. It can also be defined as a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides, making it automatically a trapezoid.

• Two opposite sides (the bases) are parallel.• The two other sides (the legs) are of equal

length. • The diagonals are also of equal length. • The base angles of an isosceles trapezoid are

equal in measure

PROPERTIES OF AN ISOSCELES TRAPEZIUM