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**Construction of Triangles : Mathematics NCERT / CBSE Revision Notes**

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**Any one of the following sets of measurements are required to construct a triangle-**

- Length of the three sides
- Two sides and the included angle
- Two angles and the included side
- Length of the hypotenuse and one side in case of a right-angled triangle.

**Construction of a triangle when measurements of its three sides are given**

Construct ΔABC, when AB = 6 cm, BC = 7 cm and CA = 9 cm.

**Steps of construction:**

Step 1: Draw line segment BC = 7 cm.

Step 2: Draw an arc with B as the centre and the radius equal to 6 cm.

Step 3: Draw an arc with C as the centre and the radius equal to 9 cm.

Step 4: Name the point of intersection of these two arcs as A.

Step 5: Join points A and B, and points A and C.

Triangle ABC is the required triangle.

**Construction of a triangle when measurements of two sides and the included angle are given**

Construct ΔPQR, when PQ = 4 cm, QR = 6 cm and ∠PQR = 60°.

**Steps of construction:**

Step 1: Draw line segment QR = 6 cm.

Step 2: Construct an angle of 60° at point Q.

Step 3: Draw an arc on the ray QX with Q as the centre and the radius equal to 4 cm.

Step 4: Name the point where the arc cuts ray QX, as P.

Step 5: Join points P and R.

Triangle PQR is the required triangle.

**Construction of a triangle, when two angles and the included side are given**

Construct ΔXYZ, when ∠ZXY = 40°, ∠XYZ = 95° and the included side XY = 8 cm.

**Steps of construction:**

Step 1: Draw line segment XY = 8 cm.

Step 2: Construct an angle of 40° at X with XY.

Step 3: Construct another angle of 95° at Y with YX.

Step 4: Name the point of intersection of the two rays as Z.

Triangle XYZ is the required triangle.

**Construction of a right-angled triangle, when the length of one side and the hypotenuse are given**

Construct a right-angled triangle LMN, with hypotenuse LN = 8 cm and side MN = 5 cm.

**Steps of construction:**

Step 1: Draw line 'l'.

Step 2: Mark a point on 'l' and name it M.

Step 3: Draw a line segment MN = 5 cm on 'l' .

Step 4: Construct a right angle LMN at M.

Step 5: Draw an arc with N as the centre and radius equal to 8 cm, such that it intersects MX.

Step 6: Mark the point of intersection as L.

Step 7: Join points L and N.

Triangle LMN is the required triangle.

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