Here we will show that the straight lines joining the extremities of the base of an isosceles triangle to the midpoints of the opposite sides are equal.
Solution:
Given: In ∆XYZ, XY = XZ, M and N are the midpoints of XY and XZ respectively.
To prove: ZN = YM.
Proof:
Statement 1. XY = XZ 2. NY = \(\frac{1}{2}\)XY. 3. MZ = \(\frac{1}{2}\)XZ. 4. NY = MZ. 5. In ∆NYZ and ∆MYZ, (i) NY = MZ. (ii) YZ = YZ. (iii) ∠XYZ = ∠XZY. 6. ∆NYZ ≅ ∆MYZ. 7. ZN = YM. (Proved) 
Reason 1. Given. 2. N is the midpoint of XY. 3. M is the midpoint of XZ. 4. from statements 1, 2 and 3. 5. (i) From 4. (ii) Common side. (iii) XY = XZ. 6. By SAS criterion. 7. CPCTC. 
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