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Construction 11.6 :

To construct a triangle, given its perimeter and its two base angles.

Given the base angles, ∠B and ∠C and AB + AC + BC, we have to construct ΔABC.

Steps of Construction :

  1. Draw a line segment XY equal to AB + AC + BC.
  2. Make ∠ LXY equal to ∠B and ∠ MYX equal to ∠C.
  3. Bisect ∠ LXY and ∠ MYX. Let these bisectors intersect at a point A .
  4. Draw perpendicular bisectors of line AX and AY
  5. Let PQ intersect XY at B and RS intersect XY at C.
  6. Join AB and AC

Thus, Δ ABC is a the required triangle

Justification

To justify, we have to prove

  1. AB + BC + AC  = XY
  2. ∠ LXY = ∠ B
  3. ∠ MYX = ∠ C

In Δ AXQ ,

PQ is the perpendicular bisector of AX,

∴ BX = BA

Similarly, we can say

CY = CA

Now, we know that

XY = XQ + BC + CY

XY = AB + BC  + AC

In Δ AXQ

Since AX = BA

∴ ∠ BAX =  ∠ AXB

Now, ∠ ABC is the exterior angle of triangle AXQ

∠ ABC = ∠ BAX + ∠ AXB

∠ ABC = ∠ AXB + ∠ AXB

∠ ABC = 2 ∠ AXB

∠ ABC = ∠ LXY

Thus, ∠ B = ∠ LXY

Similarly, we can prove ∠ A = ∠ MYX

Hence justified

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  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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