Practical Geometry

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

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

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.

Construct an equilateral triangle whose altitude is 4.5 cm.

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

Draw an equilateral triangle whose each side is 4.5 cm.

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

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

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

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

State whether the given pair of triangles are congruent.

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

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°.

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

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