Geometric Terms and Properties of Shapes

Named by properties, not by looks

Geometry questions keep asking you to name something: an angle, a triangle, a four-sided shape, a solid. The name always comes from PROPERTIES, the facts you can check, such as how many sides are equal, which sides are parallel, how big the angles are, or how many faces a solid has. It never comes from how the shape looks or which way up it is drawn. A square turned onto its corner is still a square, because its four sides are still equal and its four angles are still right angles. A flat shape with straight sides is a polygon, and its name counts the sides: a pentagon has five, a hexagon six, a heptagon seven, an octagon eight and a decagon ten. A polygon is regular when all its sides are equal AND all its angles are equal. This module works through angles, triangles, the circle, four-sided shapes and solids, and keeps asking the same question: which property proves the name?

Angle and line words

An angle is a measure of turn, in degrees. Three angle types are named by the range they fall in, and two words describe how a pair of lines sit.

Match each angle size to its type

Two ways to name a triangle

Every triangle can be named twice: once from its sides and once from its largest angle. A full answer gives both, because each name checks a different property.

Name the triangle in full

A triangle has sides of 5 cm, 5 cm and 8 cm, and its largest angle is 106 degrees. Which name describes it fully?

• An obtuse-angled isosceles triangle
• An obtuse-angled scalene triangle
• An acute-angled isosceles triangle
• A right-angled isosceles triangle

The parts of a circle

Every circle has a centre, and the distance all the way round it is the circumference. A radius goes from the centre to the circumference. A diameter goes from the circumference, through the centre, to the circumference on the other side, so it is two radii long. A chord is any straight line joining two points on the circumference, and a diameter is just the longest chord. A tangent is a straight line outside the circle that touches it at exactly one point. Part of the circumference is an arc. The region between two radii and an arc is a sector, like a slice of pizza, and the region between a chord and its arc is a segment.

Four-sided shapes form a family

Four-sided shapes are quadrilaterals, and each type is defined by a list of properties. A parallelogram has both pairs of opposite sides parallel and equal, and its opposite angles are equal. A rectangle is a parallelogram whose angles are all right angles, so its diagonals are equal in length. A rhombus is a parallelogram whose four sides are all equal, so its diagonals cross at right angles. A square has every property of a rectangle AND every property of a rhombus. A trapezium has one pair of parallel sides. A kite has two pairs of equal sides that are next to each other, and one line of symmetry. Because the lists build on each other, one shape can carry more than one name: a square is a special rectangle and a special rhombus, and both are special parallelograms. When you name a quadrilateral, check the properties, not the picture.

Find the chord

This circle has four straight lines drawn on it. Tap the CHORD that is not also a diameter.

What a rhombus always has

Select EVERY property that a rhombus always has, however it is drawn.

• Four equal sides
• Both pairs of opposite sides parallel
• Diagonals that cross at right angles
• Four right angles
• Diagonals of equal length

Spot the false shape claims

Six claims about four-sided shapes. Tap the TWO that are false.

• Every square is a rectangle.
• Every rectangle is a square.
• Every rhombus is a parallelogram.
• A square stood on one corner stops being a square and becomes a rhombus only.
• The opposite angles of a parallelogram are equal.
• A kite has two pairs of equal sides that are next to each other.

Counting a triangular prism

A solid is described by counting three things. A FACE is a flat surface, an EDGE is a line where two faces meet, and a VERTEX is a corner where edges meet; more than one vertex are vertices. Take a triangular prism, the shape of a tent or a chocolate box with a triangle at each end. It has 2 triangular end faces and 3 rectangles joining them, so 5 faces. Each triangle has 3 edges, which makes 6, and the 3 long edges join the ends, so 9 edges altogether. Each triangle has 3 corners, so 6 vertices. The quick way to count any prism is to look at the shape of one end: the faces are 2 plus the number of sides of the end, the edges are 3 times that number, and the vertices are 2 times it.

Count the corners of a hexagonal prism

A hexagonal prism has a six-sided face at each end, joined by rectangles. How many vertices does it have?

Name each solid from its faces

Each drawing shows a 3-D solid. Use its faces and surfaces to name it.

• Cube
• Cylinder
• Cone
• Square-based pyramid
• Triangular prism
• Tetrahedron
• Sphere

Complete the polygon names

A road sign with five straight sides is a _____. A floor tile with six straight sides is a _____. A stop sign has eight equal sides and eight equal angles, so it is a _____ _____.

Identify the shape from the clues

A friend describes three shapes they cannot see in full. Use only the properties they give you.

• A four-sided shape has all four sides equal, but none of its angles is a right angle. What is it?
• A solid has 5 faces. One of them is a square, and the other four are triangles meeting at a single point. What is it?
• A four-sided shape has diagonals that are EQUAL in length and also cross at RIGHT ANGLES, cutting each other in half. What is it?

Argue that a square is a rectangle

A friend says a square cannot be a rectangle, because a rectangle has two long sides and two short sides. Explain why every square is a rectangle and also a rhombus, using properties rather than how the shapes look.

• What a rectangle has to have, and what it does not have to have
• Which of those properties a square has
• What a rhombus has to have, and why a square has that too
• Why one shape can carry more than one name