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1. Make a rough sketch before drawing the accurate figure.

2. Write the given measures on the sketch.
3. Then construct the figure according to the given measures.
There are four ways to draw a triangle. A triangle can be drawn if any one of the following sets of
measurements is given.
1. SSS Criterion: If all the three sides are given, the triangle can be drawn.
2. SAS Criterion: If two sides and an included angle are given, the triangle can be drawn.

3. ASA Criterion: If two angles and an included side are given, the triangle can be drawn.
4. RHS Criterion: If the hypotenuse and a side in a right-angled triangle are given, the triangle
can be drawn.

Remember
1. Use sharp pencil to draw thin lines. 2. Mark a point lightly but firmly.
3. Keep two or three pencils ready for use. 4. The screw of the compass should not be loose.
5. Use eraser as less as you can.

Construction of a Triangle when the Lengths of its Three Sides are Given (SSS Criterion)

If all the three sides of a triangle are given, it is necessary that the sum of two sides must be
greater than the third side. Otherwise, the construction of the triangle would be impossible.

Example 4: Construct a triangle PQR such that PQ = 4.2 cm, QR = 3.8 cm, and PR = 2.6 cm.
Solution: Draw a rough sketch of DPQR and mark the given lengths ,this R
will help us decide how to proceed.
2.6 cm 3.8 cm
Steps of construction:

1. Draw a line segment PQ of length 4.2 cm. 4.2 cm
2. With Q as centre and radius 3.8 cm (= QR), Rough Sketch
R
draw an arc.
3. With P as centre and radius 2.6 cm (= PR), 2.6 cm 3.8 cm
draw an arc to cut the previous arc at R.

4. Join PR and QR. 4.2 cm
Thus, DPQR is the required triangle. A
Example 5: Construct an equilateral triangle with side 4.5 cm.
Solution: Draw a rough sketch of equilateral DABC with given measures, this 4.5 cm 4.5 cm
will help us decide how to proceed.
B C
Steps of construction: 4.5 cm
Rough Sketch
1. Draw a line segment BC of length 4.5 cm.
A
2. With B as centre and radius 4.5 cm, draw an arc.
3. With C as centre and radius 4.5 cm, draw an arc to cut the
previous arc at A. 4.5 cm 4.5 cm

4. Join AB and AC. Thus, DABC is the required equilateral triangle
with side 4.5 cm. B 4.5 cm C

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