6lp Understanding elementary shapes &lpIntegers 6th maths lp👇👇👇

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Introduction

Line, angle, triangle, quadrilateral, polygon, and circle are examples of elementary shapes. Any complex geometrical shape can be made from these elementary shapes.

For example, a square pyramid is made up of four isosceles triangles and a square base.

A hexagonal prism is made of 6 rectangles and two hexagons.

Even elementary shapes come in different forms, like a triangle can be an equilateral triangle, an isosceles triangle, or a scalene triangle. Similarly, a quadrilateral can be a rectangle, a square, or a parallelogram.

Measuring Line Segments

The length of a line segment is measured in millimetres and centimetres.

Comparison by Observation

If we place two line segments side by side, then their lengths can be easily compared just by observing them.

Comparing using the Divider

When two line segments are nearly of the same length, we have to use a divider to compare their lengths.

Measuring using a Ruler

The ruler is marked in centimetres and millimetres. The difference between two big markings on a ruler is 1 cm, while the difference between two small markings on the ruler is 1 mm.

Measure the line segment by keeping the ruler along the line segment with the zero of the ruler placed at one endpoint of the line segment. The reading of the other endpoint on the ruler gives the length of the line segment.

Measuring using a Ruler and a Divider

First, take the divider and with its arms stretched, fix it across the endpoints of the line segment.

Then, lift the divider and put on the ruler so that one of the arms of the divider coincides with the zero of the ruler. Take the reading from the other arm of the divider.

Right Angle

Acute Angle

Angles smaller than right angles (90 degrees) are called acute angles.

Obtuse Angle

Angles greater than right angles (90 degrees) but smaller than a straight angle are called obtuse angles.

Straight Angle

A straight angle is formed when the rays forming the angle point in exactly opposite directions. A straight angle is equal to 180°.

Reflex Angle

An angle that lies between 180° and 360° is called a reflex angle.

Complete Angle

A complete angle is formed when one complete turn or rotation is made by an arm of the angle with respect to the base arm. A complete angle is equal to 360 °.

A reflex angle measures between 180° and 360°. We cannot directly measure a reflex angle using a protractor, as the maximum it can measure is 180°. So the reflex angle is measured indirectly.

The pair of arms of an acute/obtuse angle also form a reflex angle on opposite side. In that case, the measure of the acute/obtuse angle = 360° − measure of reflex angle.

Measuring Straight and Complete Angle

A straight angle measures 180°. Using a protractor, the straight angle can be measured to show the reading of 180°. A complete angle has the measure of 360° or twice the measure of a straight angle.

Perpendicular Bisectors

A bisector is a line that divides another line segment into two equal parts. A line is said to be perpendicular to another line if it makes an angle of 90° with it. The lines are then said to be perpendicular lines.

A perpendicular bisector of a line segment must be perpendicular to it and also divide it into two equal parts.

In the following example, the bisector is not perpendicular to XY, so it is not a perpendicular bisector.

Isosceles Triangle

Scalene Triangle

In a triangle, if the lengths of the sides are different or unequal, then such a triangle is called a scalene triangle. All its three angles are unequal too.

Rhombus

All rhombuses are parallelograms, but all parallelograms are NOT rhombuses.
All squares are rhombuses, but all rhombuses are NOT squares.

Trapezium

A trapezium is a quadrilateral where there is a pair of parallel opposite sides.

Quadrilateral

Any four-sided figure is called a quadrilateral. Rectangles, squares, trapeziums, parallelograms and rhombuses are all special types of quadrilaterals. A four-sided figure in which no sides or angles are equal is a generic quadrilateral.

Diagonals of Quadrilaterals

Diagonals of a rectangle and a square are equal.
Diagonals of a parallelogram and a rhombus are not equal.
Diagonals of a square and a rhombus are perpendicular to each other.
Diagonals bisect each other in a rectangle, square, parallelogram, and a rhombus.

Diagonal Pentagon Diagonal Hexagon Triangular Prism

Prisms can be formed from rectangular bases, square bases, pentagonal bases, and hexagonal bases.

A rectangular prism is a cuboid only and square prism is a cube only.

Square Pyramid

It is 3D shape made out of square and triangular shapes. It has a square base and 4 triangular faces. It has 5 faces, 8 edges, and 5 vertices.

Triangular Pyramid or Tetrahedron

It is a 3D shape that is made from four triangular shapes. It has 4 triangular faces, 6 edges, and 4 vertices.

Cylinder, Cone, and Sphere

Cylinders, cones, and spheres are the 3D shapes that do not have straight edges.

A cylinder is made from two circles and a rectangle. It has two circular bases.
A cone is made of a circular base and a sector
A sphere has no base, face, edge, and vertex. A sphere is a 3D version of a 2D circle.