# Construction of a Triangle

A triangle is a three-sided closed figure. The sum of interior angles of a triangle is equal to 180 degrees. These angles can be equal, unequal or maybe 90 degrees. Similarly, the sides of a triangle can be equal or unequal. We can construct a triangle by using triangle properties- SAS (side angle side), SSS (side side side), ASA (angle side angle), or RHS (right angle hypotenuse side). We need to have a protractor, compass, and ruler to construct a triangle.

## Constructing a triangle with SSS property

1. Take a ruler and a compass.

2. Draw a line segment of length equal to one side of a triangle. Name it PQ.

3. Mark the value on the compass that you want to construct as a side of a triangle.

4. Place the compass on point P, draw an arc above the line.

5. Measure another side on the compass with the help of a ruler.

6. Place the compass on Q, and mark an arc above.

7. The point where two arcs meet, name it R.

8. Draw lines from PQ and QR.

9. Therefore, the required triangle is the required triangle.

## Construction of a triangle using SAS property

1. Draw a line segment of the length you want to draw as a side of a triangle. Name it XY.

2. Place a protractor on X, draw the angle, and extend the line to a specific limit.

3. Measure the side on the compass that you want as the side of a triangle.

4. Place the compass on Y, and draw an arc. Make sure the arc intersects the angular line you have constructed. If it does not intersect, then extend the lines. Name the intersection point as Z. Join YZ.

5. Therefore, triangle XYZ is the required triangle with SAS property.

## Construction of a triangle using ASA property

1. Draw a line segment of length equal to the side of a triangle, say AB.

2. Place the protractor on point A, and mark the angle of the required value.

3. Draw the line of this angle, and extend it up to a specific limit.

4. Take another point B, and perform the same steps. Extend the other line and join both of them. The point where they meet, name it C.

5. Thus, the triangle ABC is the required triangle with ASA property.

## Construction of a triangle using ASA property

1. Draw a line segment of length equal to the side of a triangle, say AB.

2. Place the protractor on point A, and mark the angle of the required value.

3. Draw the line of this angle, and extend it up to a specific limit.

4. Take another point B, and perform the same steps. Extend the other line and join both of them. The point where they meet, name it C.

5. Thus, the triangle ABC is the required triangle with ASA property.

## Construction of a triangle using RHS property

1. Draw a line segment of length equal to the hypotenuse of the triangle you want to construct. Name it AB.

2. Draw an angle of 90˚ from point A.

3. Choose the length on the compass equal to the length you want the side to be.

4. Place the compass at point A, and draw an arc. Extend the line that you have drawn for the angle and the side.

5. Join point B and the line you have constructed with 90˚. Name the intersection as C.

6. Therefore, the triangle ABC is the required triangle with the RHS property.

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