Properties of polygons
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1 Higher heck In Properties of polygons 1. Triangle PQR is isosceles with PR = QR. ngle PQR = 57. Find angle QRP. 2. D is a rhombus. If D = 18, calculate the size of. D 3. Find the size of angle x in the diagram below. x E D In a triangle, the first angle is a right angle and the second angle is 5 times the size of the third angle. Find the size of all three angles. 5. Work out the size of each angle in the quadrilateral below. 4(x 1) 3(x 4) 6. Show that triangle MPQ is isosceles. P N 35 Q M
2 7., and are points on the circumference of a circle, centre. Given that the =, prove that =. 8. Points, and are on the circumference of the circle, centre. y considering the triangles and, prove that the obtuse angle = 2(x + y). y x 9. Points, and are on the circumference of the circle, centre. Given that =, find the value of angle. 10. Points, and are on the circumference of the circle, centre. None of the chords, or go through the centre of the circle. DE is a tangent and touches the circle at point. Find the of the radius of the circle. D 38 E 6 cm
3 Extension ut out and arrange the decision boxes to form a flow chart for distinguishing between quadrilaterals (square, parallelogram, trapezium, rectangle, kite, rhombus and nonspecific general quadrilateral). re all the angles equal? Is there exactly one line of symmetry? re the opposite angles equal? re there parallel sides? re all the sides equal? re there equal adjacent sides?
4 nswers x = , 15 and , 108, 72, Given that NQ = QP, QNP = QPN = 35 NQP = 180 ( ) = 110 (sum of angles in a triangle is 180 ). Given that NPM = 90, QPM = = 55 and NMP = 180 ( ) = 55 (sum of angles in a triangle is 180 ). QPM = NMP triangle MPQ is isosceles. 7. = = as they are radii of the circle triangles and are isosceles triangles and are congruent, SS so =. 8. = = as they are all radii of the circle triangles and are isosceles angle = x because base angles of an isosceles triangle are equal. Similarly angle = y, because base angles of an isosceles triangle are equal. ngle = 180 2x because sum of angles in a triangle is 180. Similarly angle = 180 2y angle = 360 (180 2x) (180 2y) = 2x + 2y = 2(x + y) 9. Given = and = = (radii) then triangles and are equilateral triangles and is a rhombus. = 60 so = cm
5 Extension ne possible arrangement: re all the angles equal? re all the sides equal? square rectangle re there equal adjacent sides? Is there exactly one line of symmetry? kite rhombus re there parallel sides? re the opposite angles equal? parallelogram trapezium non-specific quadrilateral We d like to know your view on the resources we produce. y clicking on Like or Dislike you can help us to ensure that our resources work for you. When the template pops up please add additional comments if you wish and then just click Send. Thank you. Whether you already offer R qualifications, are new to R, or are considering switching from your current provider/awarding organisation, you can request more information by completing the Expression of Interest form which can be found here: Looking for a resource? There is now a quick and easy search tool to help find free resources for your qualification: s/ R Resources: the small print R s resources are provided to support the teaching of R qualifications, but in no way constitute an endorsed teaching method that is required by the oard, and the decision to use them lies with the individual teacher. Whilst every effort is made to ensure the accuracy of the content, R cannot be held responsible for any errors or omissions within these resources. We update our resources on a regular basis, so please check the R website to ensure you have the most up to date version. R This resource may be freely copied and distributed, as long as the R logo and this message remain intact and R is acknowledged as the originator of this work. R acknowledges the use of the following content: Maths and English icons: ir0ne/shutterstock.com
6 ssessment bjective Topic R G ssessment bjective Topic R G 1 1 Use the properties of an isosceles triangle to find an angle 1 1 Use the properties of an isosceles triangle 1 2 Use the properties of a rhombus 1 3 Use the properties of a trapezium and an isosceles triangle 1 4 Use the properties of a right-angled triangle 1 4 Use the properties of a right-angled triangle 1 5 Use the properties of a parallelogram 1 5 Use the properties of a parallelogram 2 6 Use the properties of an isosceles triangle in a simple proof 2 6 Use the properties of an isosceles triangle in a simple proof Use the properties of triangles in circle to find a 1 2 Use the properties of a rhombus Use the properties of a trapezium and an isosceles triangle Use the properties of triangles in circle to find a ssessment bjective Topic R G ssessment bjective Topic R G 1 1 Use the properties of an isosceles triangle to find an angle 1 1 Use the properties of an isosceles triangle 1 2 Use the properties of a rhombus 1 2 Use the properties of a rhombus 1 3 Use the properties of a trapezium and an isosceles triangle Use the properties of a trapezium and an isosceles triangle Use the properties of a right-angled triangle 1 4 Use the properties of a right-angled triangle 1 5 Use the properties of a parallelogram 1 5 Use the properties of a parallelogram 2 6 Use the properties of an isosceles triangle in a simple proof 2 6 Use the properties of an isosceles triangle in a simple proof Use the properties of triangles in circle to find a Use the properties of triangles in circle to find a 3 10
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