[Maths Class Notes] on Construction of Triangles Pdf for Exam

A triangle is a three-sided polygon that has three edges and three vertices and the sum of all the three internal angles of any given triangle is 180°. To construct a triangle, geometrical tools are needed. Using a ruler, compasses, protractor and a pencil, a triangle can be constructed. For constructing a triangle, it is important to have the following dimensions:

Before getting into the construction of a triangle, let’s know what are the properties of a triangle to keep in mind while constructing a triangle.

Properties

There are many types of triangles such as equilateral triangle, scalene triangle, acute-angle triangle, isosceles triangle, obtuse-angled triangle, right-angled triangle, but all the triangles have some common properties:

• The sum of all the internal angles of a triangle equals 180°.

• The sum of two adjacent internal angles is equal to the external angle of the opposite side.

• The sum of the lengths of any two sides of a triangle is greater than the length of the third side of the triangle.

A right-angled triangle has a property called Pythagoras theorem which states that the square of the hypotenuse side of the triangle is equal to the sum of squares of the two other sides.

Construction

Based on the dimensions given for construction, they can be classified into three categories:

• SSS – when three sides are given.

• SAS – when one angle and two sides are given.

• ASA – when two angles and one side are given.

Construction of SSS triangle

When three sides of a triangle are given, construction of a SSS triangle is possible using the following directions:

• Draw a line segment of length equal to the longest side of the triangle.

• Using a ruler, measure the length of the second side and draw an arc.

• Then take the measurement of the third side and cut the previous arc and mark the point.

• Now join the endpoints of the line segment to the point where the two arcs cut each other and get the required triangle.

Construction of SAS triangle

When two sides and an internal angle of a triangle is given then the SAS triangle can be constructed as follows:

• Draw a line segment of length equal to the longest side of the triangle using a ruler and pencil.

• Put the center of the protractor on one end of a line segment and measure the given angle. Join the points and construct a ray, such that the ray is nearer to the line segment.

• Take measurement of the other given side of the triangle using a ruler and a compass.

• Then put the compass at one end and cut the ray at another point.

• Now join the other end of the line segment to the point.

Construction of ASA triangle

When two angles and a side are given, an ASA triangle can be constructed in the following way:

• Draw a line segment of length equal to the given side of the triangle, using a ruler.

• At one endpoint of a line, segments measure one of the given angles and draw a ray.

• At another endpoint of the line segment, measure the other angle using a protractor and draw another ray such that it cuts the previous ray at a point.

• Join the previous point with both the endpoints of the line segment and get the required triangle.

Construction of a Right-Angled Triangle

When the hypotenuse of a triangle is given along with the two other sides of the triangle, a right-angled triangle can be constructed as follows:

• Draw the line segment equal to the measure of hypotenuse side

• At one of the endpoints of the line segment, measure the angle equal to 90° and draw a ray

• Then measure the length of another given side and draw an arc to cut the ray at a point and name it

• Now join the point to the other side of the line segment to get the required right-angled triangle.

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