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Question
Construct a ΔABC in which BC=6cm,∠B=30∘andAB−AC=3.4cm Justify your constructions.
Construct a ΔABC in which BC=6cm,∠B=30∘andAB−AC=3.4cm Justify your constructions.
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Solution
Steps of construction:
1. Draw a line segment BC = 6 cm.
2. Construct ∠CBX = 30°.
3. Set off BD = 3.5 cm.
4. Join DC .
5. Draw the right bisector of DC , meeting BD produced at A.
6. Join AC .
Thus, △ ABC is the required triangle.
Justification:
Point A lies on the perpendicular bisector of DC.
⇒ AD = AC
Now
BD = AB − AD = AB − AC
Steps of construction:
1. Draw a line segment BC = 6 cm.
2. Construct ∠CBX = 30°.
3. Set off BD = 3.5 cm.
4. Join DC .
5. Draw the right bisector of DC , meeting BD produced at A.
6. Join AC .
Thus, △ ABC is the required triangle.
Justification:
Point A lies on the perpendicular bisector of DC.
⇒ AD = AC
Now
BD = AB − AD = AB − AC
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