Practical Geometry — Practice

Question 1

Construct a triangle with sides 4 cm, 5 cm, 6 cm. Write the steps.

Accepted Answer

Draw the 6 cm base. From one end draw an arc of 4 cm, from the other an arc of 5 cm; they meet at the third vertex. Join the sides. Check: 4 + 5 > 6, so it is valid.

Question 2

Construct triangle ABC with AB = 5 cm, AC = 4 cm, angle A = 70 degrees.

Accepted Answer

Draw AB = 5 cm. At A construct a 70-degree angle. Mark C on the ray with AC = 4 cm. Join BC.

Question 3

Construct triangle PQR with PQ = 6 cm, angle P = 55 degrees, angle Q = 65 degrees.

Accepted Answer

Draw PQ = 6 cm. At P construct 55 degrees and at Q construct 65 degrees; the rays meet at R. (Angle R = 60 degrees.)

Question 4

Construct a right triangle with hypotenuse 7 cm and one side 4 cm.

Accepted Answer

Draw the 4 cm side, erect a perpendicular at one end, then with the other end as centre draw a 7 cm arc cutting the perpendicular. Join to complete.

Question 5

Can a triangle with sides 2 cm, 3 cm, 6 cm be constructed? Why?

Accepted Answer

No. 2 + 3 = 5, which is not greater than 6, so the triangle inequality fails and the arcs would not intersect.

Practice — Practical Geometry

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