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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.

Given: In ∆ABC, BC = 8 cm, ∠B = 45° and AB – AC = 3.5 cm.
Required: To construct the triangle ABC.
Steps of Construction:
1. Draw the base BC = 8 cm.

2. At the point B make an angle XBC = 45°.
3. Cut the line segment BD equal to AB – AC (= 3.5 cm) from the ray BX.
4. Join DC.
5. Draw the perpendicular bisector, say PQ of DC.
6. Let it intersect BX at a point A.
7. Join AC.
Then, ABC is the required triangle.

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