Points, lines, angles


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1 Points, lines, angles Point Line Line segment Parallel Lines Perpendicular lines Vertex Angle Full Turn An exact location. A point does not have any parts. A straight length that extends infinitely in both directions. It has no width. Part of a line. Straight lines that will never meet Straight lines that meet at 90 degrees. A point where two lines meet. Also called corner. The measure of turn between two straight lines that meet at a point is 360 (360 degrees) Quarter Turn is 90 Half Turn is 180 3/4 Turn is 270 Acute angle An angle less than 90 degrees (x < 90). Right angle An angle of exactly 90 degrees (x = 90) Obtuse angle An angle of more than 90 degrees and less than 180 degrees (90 < x < 180) Reflex angle An angle of more than 180 degrees but less than 360 degrees. (180 < x< 360) ABC Indicates the angle with vertex at B, between the lines AB and BC. Adjacent angles Adjacent means next to. Adjacent angles share a common vertex and a common side. They are next to each other and do not overlap. Adjacent angles around a point add up to 360 degrees Adjacent angles on a straight line add up to 180 degrees Opposite angles created by two straight intersecting lines are equal
2 Parallel lines Parallel Lines Transversal Alternate Cointerior Supplementary Complementary Straight lines that will never meet. Indicated by arrows A line that cuts two parallel lines If we move one parallel line on top of another, corresponding angles lie on top of each other. angles are equal. Alternate angles are between a pair of parallel lines and on opposite sides of the transversal. Alternate angles are equal. Cointerior angles are between a pair of parallel lines and on the same side of the transversal. Cointerior angles add up to 180 degrees. Any pair of angles that add up to 180 degrees. Any pair of angles that add up to 90 degrees. bearings Bearing An angle measured clockwise from North. 045 All bearings are given using 3 digits, adding a zero at the front if necessary. Bearing of A from B from b means we should start at B, face north, turn clockwise, until we face A. Triangles & quadrilaterals Interior Angle Triangle Angle Sum Proof of angle sum Equal Sides Equilateral Triangle Isosceles Triangle Scale Triangle Right Triangle Quadrilateral The interior angles of a shape are those created at the corners of the shape. The interior angles in a triangle add up to 180 degrees. To prove the angles will always add up to 180 degrees, draw the triangle inside a pair of parallel lines. You can then see the angles add up to a straight line. Equal length sides are shown with a single or double dash. A triangle with all sides and all angles equal A triangle where two sides are equal and two angles are equal. None of the angles or sides are equal A triangle that contains a right angle. Can be scalene or isosceles. Closed figure with 4 straight sides. Shortened to quad. Quad Angle Sum 360 0
3 Special quadrilaterals Quadrilateral Parallel Sides Equal Sides Diagonals Parallelogram (opposite) Opposite corners are equal Cut each other in half Rectangle (opposite) 4 right angles Equal in length. Cut each other in half Equal in length. Square All equal 4 right angles Cut each other in half. Cut corner angles in half. Rhombus All equal Opposite corners are equal Cut each other in half. Cut corner angles in half Trapezium 1 pair Kite (adjacent) 1 pair of opposite angles are equal symmetry Line of Symmetry If a shape is folded along a line of symmetry, the two halves fit exactly on top of each other. Order of rotational Symmetry The number of times a figure fits exactly on top of itself when rotated 360 Quadrilateral Line Symmetry Rotational Symmetry Parallelogam None Order 2 Rectangle 2 lines Order 2 Square 4 lines Order 4 Rhombus 2 lines Order 2 Trapezium (isosceles) None (1 line) None (None) Kite 1 line None
4 Interior & exterior angles Polygon Triangle Quadrilateral Pentagon Hexagon Heptagon or Septagon Octagon A closed figure with 3 or more straight edges 3 sided polygon 4 sided polygon 5 sided polygon 6 sided polygon 7 sided polygon 8 sided polygon Nonagon 9 sided polygon Decagon Regular Polygon 10 sided polygon A polygon with equal angles and equal sides Triangle Interior Angle Sum 180 Quadrilateral Interior 360 ngon A polygon with n sides ngon Interior (n  2) x 180 Interior Angle of a Regular ngon Exterior Angle Interior & Exterior Exterior Sum Exterior Angle of a Regular ngon (n  2) x 180 n The angle created by extending one line of a polygon further out The interior and exterior angles of a polygon are supplementary because they form a straight line. The exterior angles of a polygon always add up to 360 degrees. 360 n
5 Congruence Sides Congruent Shapes Congruent Triangles SSSAAA Test 1: SSS Included Angle Test 2: SAS AA AAA Test 3: AAS Hypotenuse Test 4: RHS These sides will match after the shape has been transformed (reflected, rotated, enlarged or translated). These angles will match when the shape they are in has been transformed. Same shape, same size. Congruent shapes fit on top of each other exactly because corresponding angles are the same size and corresponding sides are the same length. Congruent triangles have 3 corresponding sides that are equal and 3 corresponding angles that are equal. If a pair of triangles have 3 equal corresponding sides then they are congruent. SSS implies SSSAAA. The angle in between two sides. If a pair of triangles have 2 equal corresponding sides and the included angle is also equal, the triangles are congruent. SAS implies SSSAAA. If a pair of triangles have two equal angles, then they must have three equal angles. AA implies AAA. If a pair of triangles have the same three angles, they may or MAY NOT be congruent. They could be the same shape, but different sizes. If a pair of triangles have two equal angles and one corresponding side that is also equal, they are congruent. The side opposite the right angle in a triangle. If two right angled triangles both have the same hypotenuse and another corresponding side that is equal, they are congruent. similarity Similar Same shape. Similar shapes are enlargements of each other. Similar shapes have the same angles. Sides If we divide the lengths of corresponding sides, we get a constant number for similar shapes. The sides are in proportion, or constant ratio. AA If two triangles have two equal angles, they are similar
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