 # To Construct a Triangle whose Three Sides are given | How to draw a Triangle Knowing the Length of its 3 Sides?

Geometry is a branch of math that deals with constructing figures like triangles, squares, circles, etc. The construction of triangles is done using a ruler, compass, and even with the help of the protractor. The triangles can be classified based on sides and angles. A triangle consists of three sides, three vertices, and three angles. Let us discuss types of construction of triangles, steps to Construct a Triangle whose Three Sides are given with examples from here. We suggest the students of 5th Grade Math follow our page to score better grades in the exams.

### How to Construct a Triangle given all 3 Sides?

1. Say you need to construct a triangle having three sides.
2. Draw a line segment measuring one of the given side lengths of the triangle.
3. Set the width of your compass equal to another given side length.
4. Place the tip of the compass on one of the endpoints of the side AB and draw an arc on either side of the line segment AB.
5. Set the width of your compass equal to the length of the third side.
6. Place the tip of the compass on B and draw another arc that cuts the previously drawn arc at some point.
7. Join C to each of the points A and B to complete the triangle.

### Constructing a Triangle given Three Sides Examples

Example 1.
Draw a triangle QPR such that PQ = 5 cm, QR = 4.5 cm, PR = 3 cm.
Solution:
Let us follow the steps one by one to construct the triangle when three sides are given.
i. Draw a line segment PQ = 5 cm.
ii. With P as center and radius 3 cm, draw an arc.
iii. Now with Q as center and radius 4.5 cm, draw another arc cutting the previous arc at R.
iv. Join PR and QR. Therefore the QPR is the required triangle.

Example 2.
Draw a triangle ABC such that BC = 5.5 cm, AB = 3.5 cm, AC = 6 cm.
Solution:
Let us follow the steps one by one to construct the triangle when three sides are given.
i. Draw a line segment AC = 6 cm.
ii. With A as center and radius 3.5 cm, draw an arc.
iii. Now with C as center and radius 5.5 cm, draw another arc cutting the previous arc at B.
iv. Join AB and BC. Therefore the ABC is the required triangle.

Example 3.
Draw a triangle ABC such that BC = 6 cm, AB = 5 cm, AC = 7 cm.
Solution:
Let us follow the steps one by one to construct the triangle when three sides are given.
i. Draw a line segment AC = 7 cm.
ii. With A as center and radius 5 cm, draw an arc.
iii. Now with C as center and radius 6 cm, draw another arc cutting the previous arc at B.
iv. Join AB and BC. Therefore the ABC is the required triangle.

Example 4.
Draw a triangle ABC such that BC = 3.5 cm, AB = 5 cm, AC = 4 cm.
Solution:
Let us follow the steps one by one to construct the triangle when three sides are given.
i. Draw a line segment AB = 5 cm.
ii. With A as center and radius 4 cm, draw an arc.
iii. Now with B as center and radius 3.5 cm, draw another arc cutting the previous arc at C.
iv. Join AB and BC. Therefore the ABC is the required triangle.

Example 5.
Draw a triangle XYZ such that YZ = 3 cm, XY = 4 cm, XZ = 5 cm.
Solution:
Let us follow the steps one by one to construct the triangle when three sides are given.
i. Draw a line segment XZ = 5 cm.
ii. With X as center and radius 4 cm, draw an arc.
iii. Now with Z as center and radius 3 cm, draw another arc cutting the previous arc at Y.
iv. Join XY and YZ. Therefore the XYZ is the required triangle.

### FAQs on How to Draw a Triangle given Three Sides

1. When three sides of a triangle are given what type of triangle is constructed?

It is possible to draw more than one triangle that has three sides with the given lengths.

2. How do you construct a triangle given all sides?

• Draw the longest side using a ruler.
• Open the pair of compasses until they are 5 cm wide. Use a ruler to measure it. Draw an arc from point H above the line.
• Open the pair of compasses until they are 3 cm wide. Use a ruler to measure it.
• Join the arc to the points H and J using a ruler.

3. Which type of triangle is best for construction?

The equilateral triangle is by far the most common triangle used in architecture. An equilateral triangle features three congruent sides and angles measuring 60 degrees on each corner.

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