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Construction 11.4 :

To construct a triangle, given its base, a base angle and sum of other two sides.

Given the base BC, a base angle ∠B and the sum AB + AC,

we need to construct Δ ABC

Steps of Construction :

  1. Draw base BC and at point B make an angle XBC equal to the given angle.
  2. Cut a line segment BD equal to AB + AC from ray BX.
  3. Join DC. Draw perpendicular bisector PQ of line DC.
  4. Let PQ intersect BD a point A. Join AC.

Then, Δ ABC is the required triangle.

Justification

We need to prove that AB + AC = BD .

Given Base BC and ∠B

In Δ ACD,

  PQ is the perpendicular bisector of CD

i.e. AR is the perpendicular bisector of CD

⇒ CR = DR

& ∠ ARC = ∠ ARD = 90°

Now, in Δ ADR and Δ ACR

  AR = AR

    ∠ ARC = ∠ ARD

  CR = DR

∴ Δ ADR ≅  Δ ACR

⇒ AC = AD

Now,

BD = AB + AD

BD  = AB + AC

Thus, our construction is justified

-ev-

  1. Chapter 11 Class 9 Constructions
  2. Concept wise
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CA Maninder Singh
CA Maninder Singh is a Chartered Accountant for the past 7 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .
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