Practical Geometry

If one of the other angles of a right-angled triangle is obtuse, whether the triangle is possible to construct.

In ΔABC, ∠A =∠B = 50°. Name the pair of sides which are equal.

Draw a ΔABC in which BC = 5 cm, AB = 4 cm and m∠B = 50°.

What will be the other angles of a right-angled isosceles triangle?

State whether the triangle is possible to construct if

(a) In ΔABC, m∠A = 80°, m∠B = 60°, AB = 5.5 cm

(b) In ΔPQR, PQ = 5 cm, QR = 3 cm, PR = 8.8 cm

Draw an equilateral triangle whose each side is 4.5 cm.

Draw an isosceles right-angled triangle whose hypotenuse is 5.8 cm.

Construct an equilateral triangle whose altitude is 4.5 cm.

In ΔABC, ∠A = ∠B = 50°. Name the pair of sides which are equal.

Construct a ΔABC such that AB = 6.5 cm, AC = 5 cm and the altitude AP to BC is 4 cm.

Draw a ΔPQR, in which QR = 3.5 cm, m∠Q = 40°, m∠R = 60°.

What is the measure of an exterior angle of an equilateral triangle?

There are four options, out of which one is correct. Choose the correct one:

(i) A triangle can be constructed with the given measurement.

(a) 1.5 cm, 3.5 cm, 4.5 cm

(b) 6.5 cm, 7.5 cm, 15 cm

(c) 3.2 cm, 2.3 cm, 5.5 cm

(d) 2 cm, 3 cm, 6 cm

(ii) (a) m∠P = 40°, m∠Q = 60°, AQ = 4 cm

(b) m∠B = 90°, m∠C = 120° , AC = 6.5 cm

(c) m∠L = 150°, m∠N = 70°, MN = 3.5 cm

(d) m∠P = 105°, m∠Q = 80°, PQ = 3 cm

Construct a ΔPQR in which m∠P = 60° and m∠Q = 30°, QR = 4.8 cm.

State whether the given pair of triangles are congruent.

Draw ΔPQR in which QR = 5.4 cm, ∠Q = 40° and PR = 6.2 cm.