Sec 1 Quadrilaterals and Polygons

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www.ApexEducators.com 1 Name : _________________________ Date: _________________________ Secondary 1 Mathematics – Quadrilaterals and Polygons 1. Types of Polygons Number of sides Name and Drawing Number of sides Name and Drawing 3 sides 7 sides 4 sides 8 sides 5 sides 9 sides 6 sides 10 sides Note: A regular polygon has all sides of the same length and all angles are equal. The sum of interior angles of an n-sided polygon = ("−2)×180° The size of each interior angle of a regular n-sided polygon = ("#$)×'()°" The sum of exterior angles of a n-sided polygon = 360° The size of each exterior angle of a regular n-sided polygon = +,)°" Note: Interior angle + Exterior angle = 180° (supplementary angles)

www.ApexEducators.com 2 Example: Triangle The sum of interior angles of a triangle = (3−2)×180° = 1×180° = 180° The size of each interior angle of an equilateral triangle = (+#$)×'()°+ = 60° The size of each exterior angle of an equilateral triangle = +,)°+ or 180°−60° = 120° The sum of the exterior angle of an equilateral triangle = 360° Example: Rectangle The sum of interior angles of a rectangle = (4−2)×180° = 2×180° = 360° The size of each interior angle of a rectangle = (-#$)×'()°- = 90° The size of each exterior angle of a rectangle = +,)°- or 180°−90° = 90° The sum of the exterior angle of a rectangle = 360°

www.ApexEducators.com 3 2. Angle Properties of Quadrilaterals Name Description Figure Trapezium • One pair of parallel opposite sides Parallelogram • Two pairs of parallel opposite sides. • Opposite sides are equal in length • Opposite angles are equal • Diagonals bisect one another Rhombus • Two pairs of parallel opposite sides. • Four equal sides • Opposite angles are equal. • Diagonals bisect one another at 90° • Diagonals bisect the interior angles. Rectangle • Two pairs of parallel opposite sides. • Opposite sides are equal in length. • Diagonals are equal in length. • Diagonals bisect one another.

www.ApexEducators.com 4 Square • Two pairs of parallel opposite sides. • Four equal sides • All four angles are right angles. • Diagonals bisect each other at 90°. • Diagonals bisect the interior angles. Kite • No parallel sides • Two pairs of equal adjacent sides. • One pair of equal opposite angles. • Diagonals intersect at 90°. • One diagonal bisects the interior angles.

www.ApexEducators.com 5 Name : _________________________ Date: _________________________ Quadrilaterals and Polygons – Practice Questions 1 1. In the diagram below, determine the values of x and y. (a) Answer: x = ________________° Answer: y = ________________° (b) Answer: 0 = ________________° 1 = ________________°

www.ApexEducators.com 6 (c) Answer: 0 = ________________° 1 = ________________° (d) Answer: 0 = ________________° 1 = ________________°

www.ApexEducators.com 32 9. (a) Three of the exterior angles of a polygon with n sides are 60°, 45° and 75°. The remaining exterior angles are each 30°. Calculate the value of n. Answer: (a) n = ________________ (b) ABCDEF is a hexagon. Find the value of w. Answer: (b) w = ________________

www.ApexEducators.com 33 10. In the figure, ABCD is a trapezium. Given that DA is parallel to GF, BA is parallel to CD, CG = CF, ∠DAG = 78°, ∠FGC = 43° and ∠BFE = 35°, show that AG is parallel to EF. 11. (a) Find the interior angle of a regular 15-sided polygon. (b) An n-sided polygon has 2 interior angles measuring 100 each and the remaining interior angles are q each. Find an expression for q in terms of n. Answer: (a) interior angle = ________________ ° (b) q = ________________

www.ApexEducators.com 34 12. The diagram below is made up of a square, a regular pentagon and a regular polygon of n sides. ABCDE shows part of the n-sided polygon. Find (a) ∠89I, (b) the interior angle of n-sided polygon ∠894 (c) the number of sides n Answer: (a) ∠89I = ________________ ° (b) ∠894 = ________________ ° (c) " = ________________