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Constructions

Short Answer Type

21. Construct an equilateral triangle of side 6.6 cm. Label its vertices as A, B and C. From point C draw a median CF.

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22. Construct a ∆ABC with ∠A = 75°, ∠B = 30° and AB = 5.6 cm. Measure ∠C.

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23. Construct a triangle of sides 3 cm, 3.5 cm and 5 cm. Bisect the smallest angle of the triangle.

[Hint: The angle opposite to the side 3 cm is the smallest angle.]

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24. Construct a triangle ABC in which BC = 7 cm, ∠B = 75° and AB + AC = 13 cm.

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25. Construct a triangle ABC in which BC = 8 cm, ∠B = 45° and AB – AC = 3.5 cm.

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26.
Construct a triangle PQR in which QR = 6cm, ∠Q = 60° and PR – PQ = 2cm.

Given: In ∆PQR, QR = 6 cm, ∠Q = 60° and PR – PQ = 2 cm.
Required: To construct the ∆PQR.
Steps of Construction:
1. Draw the base QR = 6 cm.
2. At the point Q make an ∠XQR = 60°.
3. Cut line segment QS = PR – PQ (= 2 cm) from the line QX extended on opposite side of line segment QR.

Given: In ∆PQR, QR = 6 cm, ∠Q = 60° and PR – PQ = 2 cm.Require

4. Join SR.
5. Draw the perpendicular bisector LM of SR.
6. Let LM intersect QX at P.
7. Join PR.
Then, PQR is the required triangle.