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Question
Construct a ΔABC in which AB=5cm,∠A=30∘andAC−BC=2.5cm Justify your constructions.
Construct a ΔABC in which AB=5cm,∠A=30∘andAC−BC=2.5cm Justify your constructions.
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Solution
Steps of construction:
1. Draw a line segment AB = 5 cm.
2. Construct ∠BAX = 30°.
3. Set off AD = 2.5 cm.
4. Join DB.
5. Draw the right bisector of DB, meeting DB produced at C.
6. Join CB.
Thus, △ ABC is the required triangle.
Justification:
Point C lies on the perpendicular bisector of DB.
⇒ CD = BC
Now
AD = AC − DC = AC − BC
Steps of construction:
1. Draw a line segment AB = 5 cm.
2. Construct ∠BAX = 30°.
3. Set off AD = 2.5 cm.
4. Join DB.
5. Draw the right bisector of DB, meeting DB produced at C.
6. Join CB.
Thus, △ ABC is the required triangle.
Justification:
Point C lies on the perpendicular bisector of DB.
⇒ CD = BC
Now
AD = AC − DC = AC − BC
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