Equilateral Triangles

A triangle is said to be an equilateral triangle if all three sides are equal and all three angles are congruent. In an equilateral triangle the measure of each angle is 60°.

 

Constructing triangles using protractor method

For this method, you will need a protractor and a ruler. Follow the steps given below to construct an equilateral triangle of side 6 cms.

 

Step 1: Take a ruler and draw a horizontal line segment AB of length 6 cms.

 

Step 2: Now use the protractor at end A of the line segment to make an angle of 60° (every angle of an equilateral triangle measures 60°)

 

Step 3: Using the ruler, mark a point C on the line such that segment AC = 6 cms.

 

Step 4: Now complete the triangle by joining the points B and C. Measure the length of line segment BC, it should be 6 cms. Similarly, all the angles of the newly constructed triangle ABC will be of measure 60°.

 

Constructing triangles using compass method

For this method, you will need a compass and a ruler. Follow the steps given below to construct an equilateral triangle of side 6 cms.

 

Step 1: Take a ruler and draw a horizontal line segment AB of length 6 cms.

 

Step 2: Now use the compass. Place the point of the compass at end A of the line segment and set the pencil in the compass at the other endpoint B. Draw an arc from point B with A as center.

 

Step 3: Now, place the point of the compass at end B of the line segment AB and set the pencil in the compass at the other endpoint A. Draw an arc with point B as center and such that it intersects the earlier arc. Mark the point of intersection of the two arcs as point C.

 

Step 4: Use the ruler to draw line segments AC and BC. The measure of both these line segments will be equal to 6 cms. Similarly, all the angles of the newly constructed triangle ABC will be of measure 60°.

 

Constructing triangles worksheet

 

Practice Questions

Q1: Construct an equilateral triangle PQR with length of 7 cm using a protractor.

Answer:

Step 1: Draw line segment PQ of length 7 cms

Step 2: Use a protractor to draw 60° angle at point P

Step 3: Mark point R such that PR = 7 cms

Step 4. Draw line segment RQ.

 

Q2: Construct an equilateral triangle ABC with side = 5 cms using a compass.

Answer:

Step 1: Draw line segment AB of length 5 cms

Step 2: Use a compass to draw an arc from point B with A as center

Step 3: Draw an arc from point A with B as center. Mark C as the point of intersection of the two arcs

Step 4: Draw line segments AC and BC

 

 
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