Δ ABC ~ Δ ADE, In Δ ABC, AB = 6.3 cm, &ang; CAB = 50°, AC = 5.6 cm, and `"AB"/"AD" = 7/5`, Construct Δ ADE.

Steps to construct Δ ADE: Draw a line segment AB = 6.3 cm. At point A, construct &ang;CAB = 50°. On the ray AC, mark AC = 5.6 cm to locate C. Join BC to obtain ΔABC. From A, draw a ray making an acute angle with AB. On this ray, mark 7 equal segments using a compass and label them A1, A2, A3, A4, A5, A6, A7. Join A7 to B. Through A5, draw a line parallel to A7 B meeting AB at D. Through D, draw a line parallel to BC meeting AC at E.

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Maharashtra State BoardSSC (English Medium) 10th Standard

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Δ ABC ~ Δ ADE, In Δ ABC, AB = 6.3 cm, ∠ CAB = 50°, AC = 5.6 cm, and "AB"/"AD" = 7/5, Construct Δ ADE. - Geometry Mathematics 2

Question

Δ ABC ~ Δ ADE,

In Δ ABC, AB = 6.3 cm, ∠ CAB = 50°, AC = 5.6 cm, and `"AB"/"AD" = 7/5`,

Construct Δ ADE.

Diagram

Solution

Steps to construct Δ ADE:

Draw a line segment AB = 6.3 cm.
At point A, construct ∠CAB = 50°.
On the ray AC, mark AC = 5.6 cm to locate C.
Join BC to obtain ΔABC.
From A, draw a ray making an acute angle with AB.
On this ray, mark 7 equal segments using a compass and label them A₁, A₂, A₃, A₄, A₅, A₆, A₇.
Join A₇ to B.
Through A₅, draw a line parallel to A₇ B meeting AB at D.
Through D, draw a line parallel to BC meeting AC at E.