Checking understanding of angles from KS2

Maths

This unit gives pupils the opportunity to explore polygons and begin to generalise their understanding of interior/exterior angles in regular polygons. In the future unit, pupils will use the geometrical properties of a rhombus to perform various constructions

In this unit, pupils learnt how to calculate with angles at a point and angles on a straight line. In this unit, pupils extend their knowledge about angles in lines

In this unit pupils will investigate internal and external angles of polygons and angles made with a transveral and parallel lines. Pupils will develop their ability to formally prove properties of polygons to generalise.

Geometrical properties: polygons

Vertical angles are pairs of opposite angles formed when two lines intersect at a point. They are equal.

A vertex is the point where two or more line segments meet. The plural is vertices.

Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions.

Securing understanding of angles from KS2

Equilateral triangles have three equal-sized angles and three edges of equal length. They are regular triangles.

Scalene triangles have three different-sized angles and three different-sized edges (sides).

Isosceles triangles have two equal-sized angles and two sides of the same length.

A right-angled triangle has exactly one 90° interior angle.

Formalising understanding of triangles from KS2

A line is a straight 1D figure that does not have a thickness, and it extends forever in both directions.

A ray is a part of a line with a fixed starting point that extends forever in one direction.

A line segment is a part of a line with a fixed start point and a distinct fixed end point.

Formal angle notation

Corresponding angles are a pair of angles at different vertices on the same side of a transversal in equivalent positions.

A transversal is any line that intersects two or more lines at distinct (different) points (line, line segment or ray).

Corresponding angles

A pair of angles both between or both outside two line segments that are on opposite sides of the transversal that cuts them.

Alternate angles

Co-interior angles are on the same side of the transversal line and in between the two other lines.

Co-interior angles

Two lines are parallel if they are straight lines that are always the same (non-zero) distance apart.

a pair of angles both between or both outside two line segments that are on opposite sides of the transversal that cuts them.

o-interior angles are on the same side of the transversal line and in between the two other lines.

Angles on parallel lines traversed by a straight line

The sum of the interior angles of any triangle

an angle formed inside a polygon by two of its edges.

the total when numbers are added together.

Using the sum of the interior angles of a triangle

A polygon is a flat (2D), closed figure made up of straight line segments.

An interior angle is an angle formed inside a polygon by two of its edges.

The sum is the total when numbers are added together.

Interior angles of a polygon

Deriving the sum of interior angles in multiple ways

an angle on the outside of a polygon between an extension of an edge and its adjacent edge.

Exterior angles of polygons

A regular polygon has sides that are equal and interior (inside) angles that are all equal.

An exterior angle is an angle on the outside of a polygon between an extension of an edge and its adjacent edge.

Interior and exterior angles of regular polygons

A pair of angles at different vertices on the same side of a transversal in equivalent positions.

Geometrical properties: polygons

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These lessons will be removed by end of Summer Term 2025.