Geometric Properties and Constructions

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infoWhy this? Geometric properties and constructions develop precise language, spatial reasoning, and the ability to represent relationships accurately. Work with lines, circles, scale, three-dimensional shapes, congruence, and similarity connects practical drawing with deductive geometry.

scheduleWhy now? At the end of Year 7, this unit draws together earlier learning about transformations, angles, ratio, and measurement. It establishes the properties and practical techniques needed for formal similarity, congruent constructions, and more advanced geometry.

Parallel lines are straight lines in the same plane that never meet, however far they are extended, and they stay the same distance apart.
Perpendicular lines intersect to make a right angle of `90^\circ`.
A right angle measures `90^\circ`, an acute angle is less than `90^\circ`, and an obtuse angle is greater than `90^\circ` but less than `180^\circ`.
The centre of a circle is the point that is the same distance from every point on the circumference.
A radius is a line segment from the centre of a circle to the circumference.
A diameter is a line segment that passes through the centre of a circle and joins two points on the circumference.
The diameter of a circle is twice the length of the radius.
The circumference is the boundary or perimeter of a circle.
A scale drawing represents a real object or distance in proportion, using the same ratio for every corresponding length.
On a map or scale drawing, a scale such as `1 : 1000` means 1 unit on the drawing represents 1000 of the same units in real life.
To use a scale correctly, the measurements must be in the same units before converting between drawing length and real length.
A face is a flat surface on a three-dimensional shape, an edge is where two faces meet, and a vertex is a corner where edges meet.
A cube has 6 faces, 12 edges, and 8 vertices, and a cuboid also has 6 faces, 12 edges, and 8 vertices.
For convex polyhedra, the number of faces and vertices is related to the number of edges by Euler’s formula `F + V = E + 2`.
Congruent shapes are exactly the same shape and size, so their corresponding sides and angles are equal.
Similar shapes have the same shape but not necessarily the same size, so their corresponding angles are equal and their corresponding sides are in the same ratio.

rocket_launchYou must be able to

Draw a line parallel to a given line using a ruler, keeping the new line straight and the distance between the lines constant.
Measure or construct a right angle with a protractor and draw a line perpendicular to a given line so that the angle formed is `90^\circ`.
Label the centre, radius, diameter, and circumference on a circle diagram accurately.
Use the fact that the diameter is twice the radius, or the radius is half the diameter, to find a missing circle measure.
Interpret a map scale or scale drawing by converting measurements into the same units and calculating the real distance or scaled distance correctly.
Count the faces, edges, and vertices of a three-dimensional shape systematically from a diagram or model and check the result using `F + V = E + 2` for a convex polyhedron.
Decide whether two shapes are congruent by comparing corresponding side lengths and angles, including shapes that have been rotated, reflected, or translated.
Decide whether two shapes are similar by checking that corresponding angles match and that corresponding side lengths have a constant scale factor.

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