Maths Study PDF

Topic 1: Angles Relationships Topic Breakdown: use relevant notations language and conventions for angle relationships, including parallel and perpendicular lines describe and identify geometrical properties for angles at a point apply properties of parallel lines cut by a transve...

Topic 1: Angles Relationships Topic Breakdown: use relevant notations language and conventions for angle relationships, including parallel and perpendicular lines describe and identify geometrical properties for angles at a point apply properties of parallel lines cut by a transversal to solve problems determine and justify whether 2 lines are parallel use given information to find sizes of unknown angles in a visual representation Notes Angles are measured in degrees We use the angle sign to name angles Key Terms Arm - Angles have two rays meeting at a vertex Vertex - where the arms of the angle meet Arc - circle thing that shows the degree of the angle and connects the arms over the vertex // Parallel - equal lines (Parallel lines will never meet). | Perpendicular - Perpendicular lines meet at 90° (right angles). - Statements to show parallel and perpendicular lines include the letter of the ray, the symbol followed by the letter of the other ray. Complementary angles - any to angles that add up to 90º Supplementary angles - any two angles that add up to 180º Do not need to be adjacent Adjacent angles - share a common vertex and common arm/ray Intersecting lines Types of Angles Acute - Less than 90º Right angle - 90º Obtuse angle - More than 90º, but less than 180º Straight angle - 180º Reflex angle - More than 180º, but less than 360º Revolution angle - angle of 360º Naming Angles (always use capital letters) To name an angle we need to know the letter at the vertex. To write an angle you use the angle sign followed by the letter at the vertex. Sometimes you need to specify one angle when there are many so we use three letters. The vertex letter goes in the middle and the other two letters are from the surrounding arms of the angle. Substitution If the size of the angle is unknown, we can write a pronumeral to take its place.Each statement should be followed with a reason stating the geometrical property used. Angles at a Point Angles at a point that add up to 360 are also called ‘Angles in a Revolution’. Vertically Opposite Angles Vertically opposite angles occur on either side of the point where two straight lines intersect. Vertically opposite angles are equal. Transversal Lines When a transversal cuts two or more lines, the angles formed are given certain names, nd are in the shape of a letter. Letters may be rotated or flipped around. Corresponding angles F Alternate angles Z Cointerior angles C You must ALWAYS write out the reasons in the following ways: Alternate angles are equal on parallel lines Corresponding angles are equal on parallel lines Cointerior angles add to 180° on parallel lines Topic 2: Algebraic Techniques