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Standard VI

Mathematics

Construction of a Triangle ABC with Given Base, Base Angle and Difference between Two Sides AB & AC, with AB >AC

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Question

Construct a triangle ABC in which base $A B = 5 c m, ∠ A = 30^{0} a n d A C - B C = 2.5 c m$

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Solution

Steps of Construction

Step 1 : Draw base AB = 5 cm

Step 2 : Draw $∠ B A X = 30^{o}$

Step 3 : From point A, on ray AX, cut off line segment AD = 2.5 cm (= AC – BC).

Step 4 : Join BD.

Step 5 : Draw the perpendicular bisector of BD which cuts AX at C.

Step 6 : Join BC to obtain the required triangle ABC.

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Construct a triangle ABC in which base AB=5cm,∠A=300andAC–BC=2.5cm

Steps of Construction Step 1 : Draw base AB = 5 cm Step 2 : Draw ∠BAX=30o Step 3 : From point A, on ray AX, cut off line segment AD = 2.5 cm (= AC – BC). Step 4 : Join BD. Step 5 : Draw the perpendicular bisector of BD which cuts AX at C. Step 6 : Join BC to obtain the required triangle ABC.

Construct a triangle ABC in which base $A B = 5 c m, ∠ A = 30^{0} a n d A C - B C = 2.5 c m$