Construction of a Similar Triangle, When One Vertex Is Common
Question 5 Dr...
Question
Question 5 Draw a ΔABC in which AB = 5 cm , BC = 6 cm and ∠ABC=60∘. Construct a triangle similar to ABC with scale factor 57. Justify the construction.
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Solution
Steps of construction
1. Draw a line segment AB= 5 cm 2. From Point B, draw∠ABY=60∘on which take BC = 6cm 3. Join AC, ΔABC is the required triangle. 4. From A, draw any ray AX downwards marking an acute angle. 5. Mark 7 points B1,B2,B3,B4,B5,B6 and B7on AX. Such that AB1=B1B2=B2B3=B3B4=B4B5=B5B6=B6B7 6. Join B7B and from B5 draw B5M∥B7B intersecting AB at M 7. From point M drawMN∥BCintersecting AC at N. then ΔAMNis the required triangle whose sides are equal to 57of the corresponding sides of the ΔABC Justification Here B5M∥B7B (by construction)