# Angle Properties

In this unit of work students are introduced to a range of angle properties including angles on a straight line, in a triangle and vertically opposite.  Students are guided to discover each of the angle properties for themselves so they can link them together later on.

This unit takes place in Term 5 of Year 7 and is the prerequisite unit for angles in parallel lines and exterior angles in polygons which students cover in Year 8.

##### 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 total 180°
• other multiples of 90°
• recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles.

##### Key Concepts
• Protractors have two scales measuring 0° to 180°.  One scale goes clockwise the other anti-clockwise.  Students should always start measuring from the line that goes through 0°.
• A right-angle is termed perpendicular and is 90°.
• A straight line is 180°.
• Angles about a point have a total of 360°.
• Vertically opposite angles are equal to each other.
• Angles in a triangle have a sum of 180°.
• A quadrilateral is made up of two adjoining triangles and therefore has a sum of 360°.

##### Working mathematically

Develop fluency

• Use language and properties precisely to analyse 2-D shapes
• Select and use appropriate calculation strategies to solve increasingly complex problems

Reason mathematically

• Make and test conjectures about patterns and relationships; look for proofs or counter-examples
• Begin to reason deductively in geometry, including using geometrical constructions

Solve problems

• Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems

##### Subject Content

Shape

• Draw and measure line segments and angles in geometric figures, including interpreting scale drawings
• Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
• Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon

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