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POLYGONS (Chapter 10) Mathematics for Australia Year 7 - Homework CHAPTER 10: POLYGONS 10A c POLYGONS d REMINDER A polygon is a closed plane figure with straight line sides which do not cross over. 4 Draw a freehand sketch of: a a convex 5-sided polygon 1 Which of these figures can be classified as a polygon? Give a reason if the figure is not a polygon. a b a non-convex quadrilateral b c REMINDER A regular polygon has all sides of equal length and all angles of equal measure. d 5 Explain why these figures are not regular polygons: a e b 2 What special name is given to a polygon with five sides? REMINDER A convex polygon is a polygon with no interior reflex angles. 6 a Draw a freehand sketch of a convex hexagon, and draw all of its diagonals. 3 Name these polygons according to their number of sides and whether they are convex: a b b How many diagonals does a hexagon have? 61 1 Mathematics for Australia Year 7 - Homework 10B POLYGONS (Chapter 10) b TRIANGLES REMINDER A triangle is: ² equilateral if its sides are all equal in length ² isosceles if at least two of its sides are equal in length ² scalene if none of its sides are equal in length. c 1 Measure the lengths of the sides of these triangles. Use your measurements to classify each as equilateral, isosceles, or scalene. a 3 The following diagrams are not drawn to scale, but the information marked on them is correct. Classify each triangle using at least two descriptive words. a b b c c REMINDER A triangle is: ² acute angled if all of its angles are acute ² right angled if one of its angles is a right angle (90± ) ² obtuse angled if one of its angles is obtuse. d 2 Measure the sizes of the angles of these triangles. Use your measurements to classify each as acute, obtuse, or right angled. a 10C ANGLES OF A TRIANGLE REMINDER The sum of the angles in a triangle is 180± . 61 2 POLYGONS (Chapter 10) Mathematics for Australia Year 7 - Homework 1 Find x in the following: a 3 Find the unknowns in these triangles, giving brief reasons for your answers: a 35° x° 70° a° 65° a° b x° b 136° 62° b° b° c 64° c x° 52° 3c° 2c° c° REMINDER The exterior angle of a triangle is equal to the sum of the two interior opposite angles. 4 Find x in the following: a a° x° b° 56° x± = a± + b± (x + 12)° 2 Find x in the following: a x° b 74° 86° x° 2x° b (x - 15)° c 32° x° 106° x° (x + 10)° c (3x - 25)° x° 118° 139° 61 3 Mathematics for Australia Year 7 - Homework 10D POLYGONS (Chapter 10) f ISOSCELES TRIANGLES 23° REMINDER x° An isosceles triangle has at least two sides equal in length. In any isosceles triangle: ² the base angles are equal ² the line joining the apex to the midpoint of the base is perpendicular to the base. 2 In each of the following triangles, find the value of x. Hence deduce something about the triangle. a A 38° B 1 Find the unknowns in the following which have not been drawn to scale: a (2x + 28)° x° C 46° b P x° Q 3x° 126° 4x° b R x° 40° 10E c REMINDER x cm 4 cm QUADRILATERALS A quadrilateral is a polygon with four sides. 50° 50° 1 Match each quadrilateral name with the most appropriate description. parallelogram d rectangle #bluebox#22.79651#6.72481 square x° #bluebox#12.45361#5.90108 rhombus #bluebox#16.15866#6.72481 trapezium #bluebox#17.33247#6.72481 #bluebox#15.58206#6.72481 kite #bluebox#8.55122#6.72481 a A .................................. is a quadrilateral which has exactly one pair of opposite sides parallel. 118° b A .................................. is a quadrilateral in which all sides are equal. c A .................................. is a quadrilateral which has two pairs of adjacent sides equal. e 8 cm x° 75° d A .................................. is a quadrilateral which has opposite sides parallel. y cm e A .................................. is a quadrilateral in which all angles are equal and all sides are equal. f A .................................. is a quadrilateral in which all angles equal. 61 4 POLYGONS (Chapter 10) Mathematics for Australia Year 7 - Homework 2 Draw a fully labelled sketch of a rectangle. 6 Draw a diagram to fit the following instructions. Make sure you label all of the given information. ABC is a triangle where [BC] is 8 cm long, [AB] is 6 cm long, and [AB] ? [BC]. 3 True or false? Explain your answer. a All squares are rhombuses. b There are no rectangles which are also kites. 7 Find the values of the variables in these figures, giving reasons for your answers: a x cm 5 cm y cm 4 Use a ruler to help classify the following: a 12 cm b b y° x° REMINDER k reads is parallel to. 10F ANGLES OF A QUADRILATERAL ? reads is perpendicular to. 5 Using ? and k, write two statements about the following figure: A REMINDER The sum of the angles of a quadrilateral is 360± . B a° d° D C 61 5 b° c° a + b + c + d = 360 Mathematics for Australia Year 7 - Homework POLYGONS (Chapter 10) 1 Find the values of the variables, giving brief reasons for your answers: a 46° 76° 124° x° 2 Consider the following diagram: c° a° 82° b° 115° a Find the values of a and b. 89° b 75° b Hence find the value of c. b° b° c 61° c° 58° 132° c° REVIEW OF CHAPTER 10 1 Which of these figures can be classified as a polygon? d d° a d° 2d° b c 2d° 2 Use a ruler and protractor to completely classify the following triangle. You should have two descriptions. e b° 127° 127° a° f 111° 60° b° 87° 3 Find, giving reasons, the value of x: a a° 51° 63° 61 6 x° POLYGONS (Chapter 10) Mathematics for Australia Year 7 - Homework 7 Using the information on the diagram, name the figure and find the values of c and d. b 115° x° d° 98° 70° c° c x° 113° 8 Find the values of a and b in this figure, giving reasons for your answer. 86° d 50° a° x° b° 91° 79° e x° 74° 4 Find the value of x, and hence classify triangle PQR. R x° (x - 42)° P 74° Q 5 Can a parallelogram be a kite? Explain your answer. 6 Find the values of a and b. 24° a° b° 61 7