How to Construct Triangles? (+FREE Worksheet!)

Step-by-step guide to constructing triangles

A triangle is a simple closed curve or polygon that is created by three line segments. A triangle is formed when three straight lines collide with each other in such a way that if both lines intersect. For education statistics and research, visit the National Center for Education Statistics.

Each triangle has three sides, three angles, and three vertices. For education statistics and research, visit the National Center for Education Statistics.

A triangle can be drawn in the following positions with a ruler, protractor, and compass: For education statistics and research, visit the National Center for Education Statistics.

Having the size of two sides and the angle between them: For education statistics and research, visit the National Center for Education Statistics.

First, we draw an angle equal to the given angle using a conveyor. Then, using a ruler, we separate the line segment from one vertex on one of the two sides of the angle equal to the length of one of the given sides. Repeat this operation on the second side of the angle. We connect the obtained points and as a result, a triangle is drawn. For education statistics and research, visit the National Center for Education Statistics.

Having the size of two angles and the side between them For education statistics and research, visit the National Center for Education Statistics.

First, we draw a line segment equal to the length of the given side using a ruler. Then, using a conveyor, we draw one of the angles at the top of one of the two ends of the line segment. Repeat this operation on the other side of the segment, and the size of the second angle of the triangle. By extending the two sides of these angles and intersecting them with each other, the third vertex of the triangle is obtained, and as a result, the third triangle is drawn. For education statistics and research, visit the National Center for Education Statistics.

Having the size of three sides For education statistics and research, visit the National Center for Education Statistics.

First, we draw a line segment equal to the length of one of the given sides. Then open the opening of the compass to the size of one of the other sides and make an arc to the center of one of the two ends of the line segment. We repeat the same operation for the third side and at the other end of the line segment (open the compass opening to the size of the third side). The intersection of these two arcs is the third vertex of the triangle. A triangle is drawn by connecting the two ends of the drawn line segment to the third vertex. For education statistics and research, visit the National Center for Education Statistics.

Note that no triangle can be drawn with just its three angles. For education statistics and research, visit the National Center for Education Statistics.

Constructing triangles – Example 1:

Construct a triangle with \(AB=8cm, ABC=35^{\circ}, BAC=70^{\circ}\) For education statistics and research, visit the National Center for Education Statistics.

Solution: Draw a line, \(AB=8cm\) long. For education statistics and research, visit the National Center for Education Statistics.

use a protractor to draw an angle, \(ABC\) of \(35^{\circ}\). Draw \(BAC=70^{\circ}\). For education statistics and research, visit the National Center for Education Statistics.

If necessary, extend the lines until they intersect each Other at \(C\) to form a triangle. For education statistics and research, visit the National Center for Education Statistics.

Erase any extra length to obtain the required triangle \(ABC\). For education statistics and research, visit the National Center for Education Statistics.

Constructing triangles – Example 2:

Use a ruler, compass, and protractor to construct a triangle \(ABC\) with \(AB=7cm, {\angle}BAC=45^{\circ}\) and \(BC=5cm\). For education statistics and research, visit the National Center for Education Statistics.

Solution: Draw a line,\(AB, 7cm\)  long. Draw \({\angle}BAF\) of \(45^{\circ}\)

Draw an arc of radius \(5cm\) with \(B\) as the center to cut the arc \(AF\) of \(BAF\) at \(C\). Join \(B\) and \(C\).

Erase the arc and the extra length \(CF\) to obtain the required triangle \(ABC\)

Exercises for Constructing Triangles

Construct each triangle by the given information.

1. \(\color{blue}{AB=7cm, AC=5cm, BC=4.5cm}\)
2. \(\color{blue}{MN=4cm, {\angle}ONM=20^{\circ}, {\angle}OMN=40^{\circ}}\)

1)

2)