4.
Classification of the quadrilateral based on their properties Properties No Yes Yes Yes Yes It has 2 pairs of parallel lines. No No Yes No Yes Its four sides are equal. No Yes Yes Yes Yes Its opposite sides are equal. Yes Yes Yes Yes Yes It has at least 1 pair of parallel sides. Trapezium Parallelogram Rhombus Rectangle Square Type of quadrilaterals
5.
Properties No Yes Yes Yes Yes Its opposite angles are equal. No No No Yes Yes It has 4 right angles. Trapezium Parallelogram Rhombus Rectangle Square Type of Quadrilaterals
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Properties No No Yes No Yes Its diagonals are perpendicular to each other. No Yes Yes Yes Yes Its diagonals bisect each other. No No Yes No Yes Its diagonals bisect its interior angles. No No Yes No Yes Its diagonals are equal. Trapezium Parallelogram Rhombus Rectangle Square Type of quadrilaterals
Kite: two adjacent sides are of equal length and the other two sides also of equal length. This implies that one set of opposite angles is equal, and that one diagonal perpendicularly bisects the other.
Cyclic quadrilaterals: the four vertices lie on a circumscribed circle.
Tangential quadrilaterals: the four edges are tangential to an inscribed circle.
Bicentric quadrilaterals: both cyclic and tangential
Isosceles Trapezium is a quadrilateral with a line of symmetry bisecting one pair of opposite sides, making it automatically a trapezoid . Two opposite sides are parallel , the two other sides are of equal length. The diagonals are of equal length. An isosceles trapezoid's base angles are congruent .
The area of an isosceles (or any trapezium) is equal to the average of the bases times the height.
A regular pentagon is a 5 equal sided polygon and has 5 equal angles.The angles are obtuse and it is a convex polygon.The sum of its interior angles is (5-2)x180°=540°.Its one interior angle is 108°.The sum of the polygon is 360°. The area of a regular convex pentagon with side length t is given by
A pentagon is constructible using a compass and ruler.
A regular hexagon is a 6 equal sided polygon and has 6 equal angles.The angles are obtuse and it is a convex polygon.The sum of its interior angles is (6-2)x180°=720°.Its one interior angle is 120°.The sum of the polygon is 360°. Like squares and equilateral triangles , regular hexagons fit together without any gaps (three hexagons meeting at every vertex), and so are useful for constructing tessellations . The area of a regular convex pentagon with side length t is given by
The perimeter of a regular hexagon of side length “t” is 6t, its maximal diameter 2t and its maximal diameter .
The regular octagon is a 8 equal sided polygon and has 8 equal angles.The angles are obtuse and it is a convex polygon.The sum of its interior angles is (8-2)x180°=1080°.Its one interior angle is 135°.The sum of the polygon is 360°. The area of a regular convex octagon with side length t is given by
The regular decagon is a 10 equal sided polygon and has 10 equal angles.The angles are obtuse and it is a convex polygon.The sum of its interior angles is (10-2)x180°=1460°.Its one interior angle is 144°.The sum of the polygon is 360°. The area of a regular convex pentagon with side length t is given by
A regular decagon is constructible with a compass and ruler.
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