In Maths, Construction means to draw lines, shapes, or angles perfectly. We can do constructions by using dividers, scale, protractor, pencil, and compass. All these instruments will give you a perfect shape. The students who feel constructions as a difficult concept can make use of this article. In the previous articles, we have discussed how to construct a triangle with three sides, and construct a triangle with two sides and one angle, and construct a triangle with two angles and one side.

Now on this page, we are going to learn about how to construct a right-angled triangle with step by step explanation. Also, the 5th grade students can find examples on how to construct a Right Triangle when its Hypotenuse and One Side are given.

**Read More:**

- To Construct a Triangle whose Three Sides are given
- To Construct a Triangle when Two of its Sides and the included Angles are given
- To Construct a Triangle when Two of its Angles and the included Side are given

## How to Construct(Draw) a Right Angle Triangle given Hypotenuse and One Side?

There are some important steps to follow in construction to draw a right-angled triangle.

Step 1. Draw a line segment.

Step 2. Set the compass to point on the line segment.

Step 3. Make an angle with a protractor with a measure of 90°.

Step 4. Draw an arc with a compass by taking the given radius.

Step 5. Join the points and label the sides.

### Constructing a Right Angle Triangle whose Hypotenuse and One Side are given Examples

**Example 1.**

Draw a right angle triangle ABC, right-angled at A, with AB = 5 cm and BC = 8 cm.

**Solution:**

Step 1. Draw a line segment AB = 5 cm.

Step 2. Set the compass to point on the line segment with a radius of 5 cm.

Step 3. Make an angle with a protractor with a measure of 90° with A as the center.

Step 4. Draw an arc with a compass by taking the 8 cm as a radius from point B.

Step 5. Join BC and label the sides.

Thus the above figure is the required Right triangle.

**Example 2.**

Draw a right angle triangle ABC, right-angled at C, with AB = 5 cm and AC = 4 cm.

**Solution:**

Step 1. Draw a line segment AC = 4 cm.

Step 2. Set the compass to point on the line segment with a radius of 4 cm.

Step 3. Make an angle with a protractor with a measure of 90° with C as the center.

Step 4. Draw an arc with a compass by taking the 5 cm as a radius from point A.

Step 5. Join AB and label the sides.

Thus the above figure is the required Right triangle.

**Example 3.**

Draw a right angle triangle XYZ, right-angled at X, with XY = 6 cm and YZ = 8 cm.

**Solution:**

Step 1. Draw a line segment XY = 6 cm.

Step 2. Set the compass to point on the line segment with a radius of 6 cm.

Step 3. Make an angle with a protractor with a measure of 90° with X as the center.

Step 4. Draw an arc with a compass by taking the 8 cm as a radius from point Y.

Step 5. Join YZ and label the sides.

Thus the above figure is the required Right triangle.

**Example 4.**

Draw a right angle triangle ABC, right-angled at C, with AB = 9 cm and AC = 5 cm.

**Solution:**

Step 1. Draw a line segment AC = 5 cm.

Step 2. Set the compass to point on the line segment with a radius of 5 cm.

Step 3. Make an angle with a protractor with a measure of 90° with C as the center.

Step 4. Draw an arc with a compass by taking the 9 cm as a radius from point A.

Step 5. Join AB and label the sides.

Thus the above figure is the required Right triangle.

**Example 5.**

Draw a right angle triangle ABC, right-angled at C, with AC = 4 cm and AB = 7 cm.

**Solution:**

Step 1. Draw a line segment AC = 4 cm.

Step 2. Set the compass to point on the line segment with a radius of 4 cm.

Step 3. Make an angle with a protractor with a measure of 90° with C as the center.

Step 4. Draw an arc with a compass by taking the 7 cm as a radius from point A.

Step 5. Join AB and label the sides.

Thus the above figure is the required Right triangle.