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Constructions — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsConstructions5 Marks
Question
Construct an isosceles triangle whose base is $9\ cm$ and altitude $5\ cm$. Construct another triangle whose side are $\frac34$ of the corresponding sides of the first isosceles triangle.
✓

Answer



Steps of construction:
  1. Draw a line segment $BC = 9\ cm$
  2. Draw peependicular bisector $PQ$ of $BC$ Meeting it at $M.$
  3. Fron $QP$ cut-off a distance $MA = 5\ cm.$
  4. Join $AB$ and $AC.$
Thus, isosceles $\triangle\text{ABC}$ is obtained.
  1. Below $BC$, make an acute $\angle\text{CBX}.$
  2. Along $BX, $ mark off $4$ points $B_1, B_2, B_3, B_4, $ such that $BB_1, = B_1B_2 = B_1B_3 = B_3B_4.$
  3. Join $B_4C$
  4. From $B_3, $ draw $B_3C' || B_4C,$ meeting $BC $ at $C'.$
  5. From $C',$ draw $C' A' || CA$, meeting $AB$ at $A'.$
Thus, $\triangle\text{A}'\text{BC}'$ is the required triangle similar to $\triangle\text{ABC}$ Such that each side of $\triangle\text{A}'\text{BC}'$ is $\frac34\text{times}$ the corresponding side of $\triangle\text{ABC}.$

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