Shapes

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Transformations

Transformations of a figure are changed in the image or the way the figured is presented. Methods to transform figures are translation, rotation, reflection and enlargement.

Ruler and Compass Construction

Let’s learn to construct geometric figures using a ruler and compass. Shapes, angles and lines must be drawn accurately. A ruler is used for a straightedge or drawing straight lines.

Angles Theorems

We are familiar with the parts of a circle, namely radius, diameter, chords and centre. Let’s discuss circle angle theorem. What are the other properties of a circle? What is circle theorem?

Cyclic Quadrilateral

Cyclic quadrilateral is defined as a four-sided figure whose vertices lie on the circumference of a circle. A cyclic quadrilateral is a quadrilateral inscribed in a circle.

Vectors

There are two main measures: scalar and vector. Scalar is a quantity that has size but hasn’t direction (for example, time, volume, temperature). Vector is a measure that has length and direction (for example, force, acceleration, velocity).

Loci Definition

Imagine a pilot flying an aeroplane at a certain speed, direction and altitude. By satisfying all these conditions, the plane had a good flight.

Shapes, Symmetry and Tessellation

A shape is a particular form or appearance of an object. It can be a two- or three-dimensional shape. Shapes can be a polygon. A polygon is a plane figure where the sides are straight and form an angle.

Loci & Constructions

A locus is a set of points satisfying a certain condition. The term ‘locus’, however, is rarely used in exams.

Circle Theorems

A cyclic quadrilateral is a four-sided figure in a circle, with each vertex (corner) of the quadrilateral touching the circumference of the circle. The opposite angles of such a quadrilateral add up to 180 degrees.

Areas and Volumes

A prism is a shape with a constant cross section, in other words the cross-section looks the same anywhere along the length of the solid (examples: cylinder, cuboid).

Angles - Acute, Obtuse, Straight and Right

Lines AB and CD are parallel to one another (hence the » on the lines).
a and d are vertically opposite angles. Vertically opposite angles are equal. (b and c, e and h, f and g are also vertically opposite).