Practical Geometry

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

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

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°.

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 an equilateral triangle whose altitude is 4.5 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?

Draw an equilateral triangle whose each side is 4.5 cm.

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

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

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

State whether the given pair of triangles are congruent.

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

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