TRIANGLE #triangle

March 04, 2025

TRIANGLE :

Definition 1: "A triangle is a 2-dimensional geometrical shape with three side."

We also have

Definition 2 : "A triangle is a geometrical shape with 3 angles that's why we called it as a triangle ".

In the definition 1 we define triangle without using the term "angle" but we called it as a triangle.

Why?

According to definition 1 a triangle is an intersection of 3 non-parallel lines.

If any two lines are intersected there must be an angle.

So if suppose the sides of a triangle are named as I,II,III, between the pairwise intersection of 3 lines i.e. intersection of lines I & II there is one angle, similarly between II & III and between III & I there are two angles.

Area of a triangle :

The area is the region bounded by the three sides of a triangle.

Area of a triangle is generally given by A(area of the triangle ) = 1/2 x (base x height) square units.

For example if a triangle has base 3 units and height 4 units then

Area A= 1/2 x b x h

=1/2 x 3 x 4

=6 sq. units

How to construct a triangle:

A triangle is constructed according to the given measurements by using ruler and protractor etc. These are few methods to construct a triangle ASA, SAS.

Construction of ASA triangle:

Step 1: Draw the given side of the triangle using a ruler.

Step 2: Measure the angle from left end point of the given side using protractor, mark it as a cross and draw a line from the endpoint through this mark.

Step 3: Similarly repeat the step 2 to measure the angle from right end point of the given side and continue as in step 2.

Step 4: Label the sides and angles and leave the construction lines.

Construction of SAS triangle:-

Step 1: Draw the given side of the triangle using a ruler.

Step 2: Repeat step 2 as in ASA triangle.

Step 3: Measure along the line using ruler drawn from the left hand end point to the cross, mark the length of the other given side on it.

Step 4: Merge the longest side and the other given side together to produce a triangle.

Step 5: Label the sides and angles and leave the construction lines.

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