Chapter 5 · ICSE Class 6 Math

Basic Geometrical Ideas

Every angle has a name based on how wide it opens. Drag the slider and watch the angle sweep from acute to reflex.

The Angle Explorer
45°
Acute Angle
45°

Try it: pass through 90° and 180° to see Right and Straight angles.

5.1

Types of angles

An angle is formed when two rays share a common starting point (the vertex), measured in degrees (°). Angles are named based on how wide they are.

Acute
< 90°

Smaller than a right angle.

Right
= 90°

Exactly a quarter turn.

Obtuse
90°–180°

Wider than a right angle.

Straight
= 180°

A perfectly flat line.

Reflex
> 180°

Wider than a straight angle.

Everyday example — An open book lying flat forms a straight angle (180°), while a door opened partway usually forms an acute or obtuse angle depending how far it's pushed.
5.2

Types of triangles

Triangles can be classified by their sides or by their angles.

Scalene
By Sides

All three sides are different lengths.

Isosceles
By Sides

Exactly two sides are equal.

Equilateral
By Sides

All three sides are equal.

Acute Triangle
By Angles

All three angles are less than 90°.

Right Triangle
By Angles

One angle is exactly 90°.

Obtuse Triangle
By Angles

One angle is greater than 90°.

Watch out — A triangle's angles must always add up to exactly 180° — this is true no matter what type of triangle it is.
5.3

Polygons

1What is a polygon?

A polygon is a closed flat shape made of straight sides. Polygons are named based on how many sides they have.

3 sides
Triangle
4 sides
Quadrilateral
5 sides
Pentagon
6 sides
Hexagon
7 sides
Heptagon
8 sides
Octagon
🎮 Shape Summit

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