Construction of Triangles : Mathematics NCERT / CBSE Revision Notes

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

    Construction of Triangles, Mathematics Class 7, CBSE / NCERT Revision Notes
  • 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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