Chapter 10 – Practical Geometry

Triangles can be constructed and classified based on two major concepts:

1. Sides:
   Equilateral triangle: All three sides are equal.
   Isosceles triangle: Two sides are equal.
   Scalene triangle: All three sides are equal.
2. Angles:
   Acute triangle: All angles measure less than 90 degree.
   Obtuse triangle: One angle is greater than 90 degree.
   cRight triangle: One angle is equal to 90 degree.

Construct a triangle DEF, given that DE = 7.6 cm, EF = 4.5 cm, and DF = 8.6 cm.

Steps:

1. 1. Draw a line segment EF of length 4.5 cm.
   2. Draw an arc of a radius 7.6 cm with E.
   3. Draw an arc of radius 8.6 cm with F.
   4. Mark the intersection of both the arcs with point D.
   5. Join the line segment DE and DF.
   6. You will get a triangle DEF.

Construct ΔLMN with LM = 6.4 cm, LM = 5.5 cm, and ∠M = 45 degree.

Steps:

1. 1. Draw a line segment LM of length 6.4 cm.
   2. At point M, draw a line segment MX with an angle of 45 degree with LM.
   3. Take point M as the centre, measure an arc of 5.5 cm.
   4. Draw an arc of 5.5 cm that cuts MX at point Y.
   5. Join MN.
   6. ΔLMN is ready.

Construct ΔPQR with ∠P = 40o, ∠Q = 100 degree, and XY = 7.2 cm.

Steps:

1. 1. Draw a line segment PQ of length 7.2 cm.
   2. At point P, draw a ray named PA marking an angle of 40 degree with PQ.
   3. At point Q, draw an angle of 100 degree with PQ.
   4. Draw the line segment QR.
   5. Extend the ray PA to intersect QR at point B.
   6. The point at which both the lines PA and QR intersect is point B.
   7. ΔABC is now complete.

Construct ΔABC, with ∠B = 90 degree, BC = 6 cm, and AC = 10 cm.

Steps:

1. 1. Draw a line segment BC of length 6 cm.
   2. At point B, draw BX ⊥ BC, which is perpendicular to each other. 
   3. To cut BX at point A with C as the centre, draw an arc of radius 10 cm.
   4. Join AC.
   5. ΔABC is complete.