Angles and their rules.

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Presentation transcript:

Angles and their rules

Lesson Success Criteria Lesson Objective To learn about angles, in relation to points, lines, triangles, and general polygons Lesson Success Criteria Can identify different types of angles, and calculate using appropriate geometric reasoning

Geometric Reasoning The REASON for an answer is the geometric property not the arithmetic that led to the answer ALL answers must have a REASON

Geometric Language Using the correct language is extremely important. Refer to Geometric Glossary on my website. Abbreviated form is ok to use but ensure it is correct.

Angle Rules Rule Short Version Diagram 1 Angles at a point add to 360° 2 Adjacent angles on a straight line add to 180° 3 Vertically opposite angles are equal

Practice From homework book Page 187 Ex A: Finding unknown angles

Triangle Rules Rule Short Version Diagram 4 Angle sum of a triangle add to 180° 5 Exterior angles of a triangle equals the sum of the two opposite interior angles 6 Angles in an equilateral triangle are equal (to 60°)

Base angles in an isosceles triangle are equal Triangle Rules Rule Short Version Diagram 7 Base angles in an isosceles triangle are equal

Practice From homework book Page 193 Ex C: Triangles

Quadrilaterals - interior angles sum to 360°

Quadrilaterals - interior angles sum to 360°

Page 195 Ex D: Quadrilaterals Practice From homework book Page 195 Ex D: Quadrilaterals

Exterior angles of a polygon add to 360° Polygon Rules Rule Short Version Diagram 8 Exterior angles of a polygon add to 360° 9 Interior angles of a polygon Sum to (n-2) x 180 Equal to 180 – exterior angle

Practice From homework book Page 197 Ex E: Polygons

Angles and Parallel Lines Rules Short Version Diagram 10 Corresponding angles between parallel lines are equal 11 Alternate angles between parallel lines are equal 12 Co-interior angles between parallel lines add to 180°

Page 189 Ex B: Angles and Parallel Lines Practice From homework book Page 189 Ex B: Angles and Parallel Lines

Complementary Angles Two angles are called complementary angles if they add to 90°, i.e. a right angle. (they don’t need to be adjacent angles)

Supplementary Angles Two angles are called supplementary angles if they add to 180°, i.e. a straight line. (they don’t need to be adjacent angles)