 # To Construct a Right Triangle when its Hypotenuse and One Side are given | How to Draw a Right Angle Triangle given One Side, Hypotenuse?

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.

## 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.

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