Knowledge Organiser: Triangles and Quadrilaterals What you need to know: Key Terms: You need to be able to: Types of Triangles Interior Angles: angles inside the shape •Know the properties of triangles and quadrilaterals Exterior Angles: angle between the side of a shape and a line extended from the •Group quadrilaterals adjacent side according to their properties Sum: total, add all angles together •Be able to draw different Polygon: A 2D shape made with straight triangles and quadrilaterals lines 3 equal sides 2 equal sides 0 equal sides •Complete triangles and 3 equal angles (600) Quadrilateral: a four-sided polygon 2 equal angles 0 equal angles 1 right angle 2 sets of parallel sides quadrilaterals on co- 1 line of symmetry 0 lines of symmetry 3 lines of symmetry Convex Quadrilateral: a four-sided ordinate grids. polygon where every interior angle is less •Find missing angles in Angles in Triangles than 180° triangles and quadrilaterals Angles in a triangle add up to 180° Concave Quadrilateral: a four-sided Examples – calculate the missing angles polygon where one interior angle exceeds 180° ABC is an equilateral triangle Tip – work out missing Hegarty maths clip numbers Reminder: ∴ 푥 = 180 ÷ 3 = 60° angles in alphabetical order 푥 40° Triangles: 823 Plotting coordinates: (x,y) This is an isosceles triangle Quadrilaterals:824 – 826 The x coordinate is how ∴ 푏푎푠푒 푎푛푔푙푒푠 푎푟푒 푒푞푢푎푙 far across you go Angles in triangles: 485 – 487 y 180 – 40 = 140 The y coordinate is how z 140 ÷2 = 70 ° y = 70° Angles in quadrilaterals: 560 far up/down you go Z = 180 – 70 = 110° Multi step angle problems: 488 - 491 Knowledge Organiser: Triangles and Quadrilaterals What you need to know: Types of Quadrilaterals Angles in Quadrilaterals Angles in a quadrilateral add up to 360° Examples – calculate the missing angles Angles add up to 360° 100 + 70 + 30 + d = 360 200 + d = 360 360 – 200 = d 4 equal sides 2 sets of equal sides 4 equal sides 2 sets of equal sides d= 160° 4 right angles 4 right angles 2 sets of parallel sides 2 sets of parallel sides 2 sets of parallel 2 sets of parallel sides 2 pairs of equal angles 2 pairs of equal angles sides 2 lines of symmetry 2 lines of symmetry 0 lines of symmetry 4 lines of symmetry Parallelogram – opposite angles are equal g = 50° Using angles in parallel lines 50 + f = 180° (co-interior angles) f = 180 – 50 f = 130° Interior and Exterior angles Interior + Exterior angle add up to 180° 1 set of parallel 1 set of equal sides 2 sets of equal sides 2 sets of equal sides sides 1 set of parallel sides 0 parallel sides 0 parallel sides Tip – the exterior angle of a triangle is equal to the sum of the interior 0 lines of symmetry 2 pairs of equal 1 pair of equal angles 1 pair of equal angles These two angles angles at the other two vertices angles 1 line of symmetry 1 line of symmetry add up to exterior 1 line of symmetry angle. In this example = 150°.