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Question If M and N are the midpoints of XY and XZ, what fraction of the area of ∆XYZ is the area of ∆XMN? [Hint: Join XY]
Let O be the midpoint of YZ, then join M to O and N to O. According to mid point theorem, MN = \(\frac {1}{2}\) YZ, and MN is parallel to YZ. The triangle XYZ is divided into four equal triangles. So, Area of ∆XMN = \(\frac {1}{4}\) × Area of ∆XYZ.