Straight Lines Joining the Extremities of the Base of an Isosceles TriangleYour Headline

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.


Given: In ∆XYZ, XY = XZ, M and N are the midpoints of XY and XZ respectively.

Lines Joining the Extremities of the Base of an Isosceles Triangle

To prove: ZN = YM.



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)


1. Given.

2. N is the midpoint of XY.

3. M is the midpoint of XZ.

4. from statements 1, 2 and 3.


(i) From 4.

(ii) Common side.

(iii) XY = XZ.

6. By SAS criterion.


9th Grade Math

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