# Angle Properties

Scheme of work: GCSE Foundation: Year 9: Term 6: Angle Properties

#### Prerequisite Knowledge

• Know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles.
• Draw given angles, and measure them in degrees (°)
• identify:
• angles at a point and one whole turn (total 360°)
• angles at a point on a straight line and 1/2 a turn (total 180°)
• other multiples of 90°

#### Success Criteria

• use conventional terms and notations: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons and polygons with reflection and/or rotation symmetries;
• use the standard conventions for labelling and referring to the sides and angles of triangles; draw diagrams from written description
• apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles;
• understand and use alternate and corresponding angles on parallel lines;
• derive and use the sum of angles in a triangle (e.g. to deduce use the angle sum in any polygon, and to derive properties of regular polygons)

#### Key Concepts

• Understanding the basic angle properties, such as the types of angles helps students with angle measurements.
• Rather than being told (or given) angle properties students should have the opportunity to discover and make sense of them practically.
• Use the Geogebra files to demonstrate the angle properties.
• Geometric problems can often be solved using various angle properties. Encourage students to look for alternative properties.
• Demonstrate how a polygon is made up from interior triangles when calculating their angles.

#### Common Misconceptions

• When measuring angles using a 180-degree protractor, students often confuse the upper and lower scale. Understanding basic angle properties such as acute and reflex angles helps with this.
• Students often forget the definition of properties associated to angles in parallel lines.
• Exterior angles in a polygon have to travel in the same direction for the sum to be 360Â°.

## Angle Properties Resources

### Mr Mathematics Blog

#### Planes of Symmetry in 3D Shapes

Planes of Symmetry in 3D Shapes for Key Stage 3/GCSE students.

Use isometric paper for hands-on learning and enhanced understanding.

#### GCSE Trigonometry Skills & SOH CAH TOA Techniques

Master GCSE Math: Get key SOH-CAH-TOA tips, solve triangles accurately, and tackle area tasks. Ideal for students targeting grades 4-5.

#### Regions in the Complex Plane

Explore Regions in the Complex Plane with A-Level Further Maths: inequalities, Argand diagrams, and geometric interpretations.