Practical Geometry

Question

Examine whether you can construct ΔDEF such that EF = 7.2 cm, m∠E =
110° and m∠F = 80°. Justify your answer.

Answer

Given that,

m∠E = 110° and m∠F = 80°

Therefore,

m∠E + m∠F = 110° + 80° = 190°

However, according to the angle sum property of triangles, we should obtain

m∠E + m∠F + m∠D = 180°

Therefore, the angle sum property is not followed by the given triangle. And thus, we cannot construct ΔDEF with the given measurements.

Also, it can be observed that point D should lie on both rays, EX and FY, for constructing the required triangle. However, both rays are not intersecting each other. Therefore, the required triangle cannot be formed.

Sponsor Area

Examine whether you can construct ΔDEF such that EF = 7.2 cm, m∠E =
110° and m∠F = 80°. Justify your answer.

Some More Questions From Practical Geometry Chapter

Construct ΔABC such that AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm. Measure ∠B.

Construct ΔDEF such that DE = 5 cm, DF = 3 cm and m∠EDF = 90°.

Construct an isosceles triangle in which the lengths of each of its equal sides
is 6.5 cm and the angle between them is 110°.

Construct ΔABC with BC = 7.5 cm, AC = 5 cm and m∠C = 60°.

Construct ΔABC, given m∠A = 60°, m∠B = 30° and AB = 5.8 cm.

Construct ΔPQR if PQ = 5 cm, m∠PQR = 105° and m∠QRP = 40°.
(Hint: Recall angle sum property of a triangle).