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Quadrilaterals — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSQuadrilaterals1 Mark
Question
In $\triangle\text{ABC},\angle\text{A}=30^\circ,\angle\text{B}=40^\circ$ $$and $\angle\text{C}=110^\circ.$ The angles of the triangle formed by joining the mid-points of the sides of this triangle are:
  1. 70°, 70°, 40°
  2. 60°, 40°, 80°
  3. 30°, 40°, 110°
  4. 60°, 70°, 50°
✓

Answer

  1. 30°, 40°, 110°
Solution:

If in any triangle, all the mid-points (of each sides) are joined to form a triangle, then that triangle is similian to a parent triangle.
i.e.$\triangle\text{QPR}\sim\triangle\text{ABC}$
So angles of $\triangle\text{PQR}$ will be same as angles of $\triangle\text{ABC}.$
Thus, angles are 30°, 40°, 110°

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