Draw a triangle ABC in which AB = 5 cm, BC = 6 cm and ABC= 60^{\circ}.Construct a triangle similar to ABC with scale factor \frac{5}{7} . Justify the construction

Answers (1)

Solution
Given : AB = 5 cm, BC = 6 cm

Steps of construction

  1. Draw line segment AB = 5 cm
  2. draw < ABO= 60^{\circ}  B taking as a centre draw an arc of radius BC=6cm
  3. Join AC, DABC is the required triangle
  4.  From point A draw any ray A{A}'   with acute angle \angle BA{A}'
  5.  Mark 7 points B_{1},B_{2},B_{3},B_{4},B_{5},B_{6},B_{7}  with equal distance.
  6. Join B_{7}B  and form B_{5}  draw B_{5}X\parallel B_{7}B\, \, BYmaking the angle equal From point X draw XY\parallel BC intersecting AC at Y. Then, DAMN is the required triangle whose sides are equal to \frac{5}{7}  of the corresponding sides of the \bigtriangleup ABC..

Justification: Here, B_{5X}\parallel B_{7}B  [by construction]
          \therefore \frac{AX}{XB}= \frac{5}{2}\Rightarrow \frac{XB}{AX}= \frac{2}{5}
Now \frac{AB}{AX}= \frac{AX+XB}{AX}
1+\frac{XB}{AX}= 1+\frac{2}{5}= \frac{7}{5}
Also, XY\parallel BC
\therefore \bigtriangleup AXY\sim \bigtriangleup ABC
\frac{AX}{AB}= \frac{AY}{AC}= \frac{YX}{BC}= \frac{5}{7}

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