Practical Geometry is an essential branch of geometry that focuses on the construction of various shapes and sizes. This fascinating field introduces us to a wide range of two-dimensional and three-dimensional shapes and teaches us how to draw these shapes with accurate dimensions.
In our journey through practical geometry, we are going to explore:
The construction of parallel lines
The construction of triangles based on different criteria:
When we know all three sides (SSS Criterion)
When we know two sides and the angle between them (SAS Criterion)
When we know two angles and the side between them (ASA Criterion)
When we know one side and the hypotenuse of a right triangle (RHS Criterion)
Now, let's dive into these concepts and explore them step by step.
Practical Geometry – Constructing Parallel Lines
Parallel lines are lines that never intersect or meet at a single point. They extend indefinitely in both directions and are denoted by the symbol ‘||’. Examples of parallel lines in our daily life include the lanes of a highway, the lines on a notebook page, and so on.
In the realm of practical geometry, we can construct a line parallel to another line using only a ruler and compass. To understand how to draw parallel lines step by step, you can
click here
.
Practical Geometry – Constructing Triangles
A triangle is a closed shape with three sides and three angles. The properties that define a triangle include:
The sum of all three angles equals 180 degrees
The exterior angle equals the sum of the two interior opposite angles
The sum of the lengths of any two sides is greater than the length of the third side
In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides
To construct a triangle, certain conditions based on the above properties must be met, such as:
Knowing all three sides of a triangle
Knowing two sides and the angle between them
Knowing two angles and the side between them
Knowing the hypotenuse and one side of a right triangle
Constructing Triangles (SSS Criterion)
If we know the lengths of all three sides of a triangle, we can construct it easily.
Choose one side as the base of the triangle.
Use a ruler and compass to measure and draw an arc above the base representing another side.
Repeat the process for the third side, cutting the arc to find the third vertex of the triangle.
Draw a line ‘m’. Draw a perpendicular to ‘m’ at any point on ‘m’. On this perpendicular, choose a point ‘a’, 5 cm away from ‘m’. Through a, draw a line ‘l’ parallel to ‘m’.
Construct a triangle ABC, given that AB = 6 cm, BC = 7 cm and AC = 5 cm. [Use SSS Criterion]
Construct a triangle PQR, given that PQ = 4 cm, QR = 6.5 cm and ∠PQR = 45°. [Use SAS Criterion]
Construct triangle XYZ if it is given that XY = 7 cm, measure of ∠ZXY = 100° and measure of ∠XYZ = 30°. [Use ASA Criterion]
Construct a triangle LMN, right-angled at N, given that LN = 3 cm and MN = 5 cm. [Use RHS Criterion]
Practical geometry is the branch of mathematics that deals with constructions of geometrical shapes.
How can we draw a parallel line?
To draw a line parallel to another line, we should know the distance between the two parallel lines. Use the concept of equal alternate angles or equal corresponding angles in a transversal diagram to draw a line parallel to another line.
How to draw an angle in practical geometry?
To construct an angle, first we need to draw the line that will be one of the arms of the angle. Take any point and put the protractor on the line such that the center of the protractor coincides with the point on the line. And also the edges of the protractor should coincide with the line. Thus, by marking the angle on the edge of the protractor, we can construct the angle.
Are right angles 90 degrees?
A right angle is also called 90-degree angle.
How to practically draw a triangle?
There are various scenarios based on which we can construct triangles. They are SSS criterion, SAS criterion, ASA criterion and RHS criterion.