Geometry

Points are single positions in space. We show a point by a small dot and name it with a capital letter. A drawing may have many points like A, B, C.

Lines extend in both directions without end. They are straight and we show them with an arrow at each end. A line is named using two letters with arrows above, for example: AB with double arrows.

Line segments are parts of a line with two end points. They have a fixed length. We write a segment between A and B as AB with a small line above.

Rays start at one point and go on forever in one direction. A ray from A through B is written as AB with one arrow.

In practice, children learn to draw and identify these by using a ruler and by looking at simple pictures: the edge of a book is a segment, the path of a beam of light can be drawn as a ray, and the horizon is treated like a line. Being careful about endpoints helps when measuring and building other shapes.

An angle is formed when two rays meet at a common point. This common point is called the vertex. The two rays are called the sides of the angle. We usually show the angle by drawing the two rays and an arc between them to mark where the angle opens.

Angles help us describe turns and openings. For example, the way a door opens from closed to half-open is an angle that grows as the door opens more. We name an angle using three letters with the vertex in the middle, for example ∠ABC means the vertex is B and the two sides go through A and C. If the vertex is clear, we may also write ∠B.

To be careful in naming, always check which points lie on the rays and which is the vertex. Draw neat diagrams and label each point so the angle’s name is not confusing. When there are many angles at one point, three-letter names are necessary. Practice naming angles in pictures, such as the corner of a book (one angle) or angles inside shapes like triangles and rectangles. Understanding how to name angles correctly is the first step to measuring and comparing them with tools like a protractor.

Use simple examples from daily life to see angles: the hands of a clock, an open book, or a slice of pizza. Learning correct names and labels prepares students for measuring angles and solving geometry problems later.

Angles are grouped by size. A right angle is exactly the turn of a corner of a paper or a book and looks like an L. A right angle has a square marker at the corner in drawings.

An acute angle is smaller than a right angle; it is a sharp or narrow angle. An obtuse angle is larger than a right angle but less than a straight line; it looks wide and open.

These three types are easiest for Class 4. Children should learn to spot each type by sight and by using a right-angle corner (like the corner of a notebook) as a quick test. Later, when students use a protractor, they will measure the angle in degrees to check.

Practising with real objects—open a book a little (acute), halfway (right), or more (obtuse)—helps develop an intuitive sense. Clear labelling and practice drawings make identification reliable in exams and classroom tasks.

A protractor is a tool used to measure angles in degrees. It is a half-circle marked from 0° to 180° or a full circle from 0° to 360°. For Class 4 we use the half-circle protractor.

To measure an angle: place the mid-point hole of the protractor on the angle's vertex; line up the baseline of the protractor with one side of the angle; read the number on the curved edge where the other side crosses. Choose the correct set of numbers (inner or outer scale) so the reading is between 0 and 180.

To draw an angle of given degrees: draw a ray, place the protractor with its centre at the start of the ray, mark the required degree on the arc, then join the mark to the vertex to form the second ray.

Practice steps slowly and use pencil marks. Understanding how to align the protractor and choose the right scale is as important as the final number. Measuring angles makes students confident in comparing and constructing shapes accurately.

A triangle is a polygon with three sides and three angles. Every triangle has three vertices and three sides joined together. Triangles are important because many shapes and structures are made from them and they help us learn about angles and lengths.

We classify triangles in two simple ways. First, by sides: an equilateral triangle has all three sides equal and all angles equal; an isosceles triangle has two equal sides and two equal angles; a scalene triangle has all sides of different lengths and all angles different. Second, by angles: an acute triangle has all angles less than 90°, a right triangle has one 90° angle and an obtuse triangle has one angle greater than 90°.

Children should practise drawing each type using a ruler and protractor and labelling sides and angles. Notice that the three interior angles of any triangle add up to a straight angle (180°). In Class 4 this idea is introduced informally by drawing triangles and placing angles together to see they form a straight line. Examples from daily life are roof shapes, triangular road signs and slices of cake. Activities include cutting out triangles from paper, sorting them by sides and angles, and measuring their sides to check equality. These exercises build confidence with geometric language and measurement.

Quadrilaterals are four-sided polygons. Each quadrilateral has four sides and four vertices. They come in many shapes and knowing their simple properties helps to recognise them in everyday objects like windows, tiles and boards.

Some common quadrilaterals are: a square with four equal sides and four right angles; a rectangle with opposite sides equal and four right angles; a rhombus with four equal sides but angles not necessarily right; and a trapezium which has only one pair of parallel sides. Teach students to look for equal sides, right angles, and parallel sides to decide which quadrilateral they see.

Beyond quadrilaterals, polygons are named by the number of sides: pentagon (5), hexagon (6) and so on. Encourage counting sides and vertices carefully as the first step in naming a polygon. Use paper cut-outs to sort shapes by properties: place all shapes with right angles in one pile, shapes with equal sides in another. Ask students to draw each type and label its sides and angles. These hands-on activities help solidify understanding before moving on to area and perimeter calculations.

Perimeter is the distance around a shape. To find the perimeter of a polygon, add the lengths of all its sides. For a rectangle or square this becomes easy with short rules. Perimeter is a one-dimensional measure and uses units like cm or m.

Area means the amount of flat space inside a shape. In Class 4 students learn area informally by counting square units (e.g., 1 cm × 1 cm squares) that fill the shape. This prepares them for formal area formulas later.

Finding perimeter: add all sides; for a rectangle, perimeter = 2 × (length + breadth). Finding area by counting: cover the shape with unit squares on grid paper and count fully covered squares to estimate area. Partial squares are discussed as half or shaded parts for more practice.

Practical activities include measuring a book cover's perimeter, or estimating area by counting tiles on a floor. These exercises link arithmetic and measurement in a concrete way.

A circle is the set of all points at the same distance from a fixed point called the centre. The distance from the centre to any point on the circle is the radius. A diameter is a straight line that passes through the centre and joins two points on the circle; every diameter is made of two radii placed end to end.

Children should learn how to draw a circle using a compass or by tracing a round object. On the drawn circle, mark the centre with a dot and draw a radius from the centre to the edge; then draw a diameter across the centre to show it is twice the radius. Practise measuring the radius and showing how two radii form the diameter so the rule diameter = 2 × radius becomes easy to remember.

Introduce the idea of concentric circles: two or more circles sharing the same centre but having different radii. Show where circles appear in daily life—wheels, clocks, plates, rings—and discuss how knowing the centre and radius helps when we measure or draw them. Although Class 4 does not require the circumference formula, understanding parts of a circle and the simple relation between radius and diameter prepares students for later work in higher classes.

Line symmetry (mirror symmetry) means a shape can be folded along a line so the two halves match exactly. The folding line is called the line of symmetry. Simple shapes like squares, rectangles and equilateral triangles have one or more lines of symmetry.

Students learn to fold paper shapes or use tracing paper to check symmetry. Drawing the line of symmetry on a picture of a butterfly or a leaf shows how the two sides mirror each other. Some shapes have no symmetry.

Simple constructions include drawing perpendicular lines (using a corner of paper or a right-angle marker), copying a line segment with a ruler, and drawing a circle using a compass or tracing. These construction skills make geometric drawings neater and prepare children for higher classes.

Activities: fold paper butterflies, draw the line of symmetry on letters (A, H, T) and objects, and practice basic constructions using rulers and compasses under supervision.