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Construct a triangle ABC with perimeter …

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Construct a triangle ABC with perimeter 11cm and each of its base angle is 45°
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Sia ? 5 years, 5 months ago

Given: In triangle ABC, {tex}\angle{/tex}B = 45o, {tex}\angle{/tex}C = 45o and AB + BC + CA = 10 cm.
Required: To construct the triangle ABC.
Steps of construction :

  1. Draw a line segment XY = AB + BC + CA = 10 cm.
  2. Construct {tex}\angle{/tex}LXY = {tex}\angle{/tex}B = 45o and {tex}\angle{/tex}MYX = ∠C = 45o
  3. Bisect {tex}\angle{/tex}LXY and {tex}\angle{/tex}MYX. Let these bisectors meet at a point A.
  4. Draw the perpendicular bisectors PQ of AX and RS of AY.
  5. Let PQ intersect XY at B and RS intersect XY at C.
  6. Join AB and AC.


ABC is the required triangle.

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