Theorem on Isosceles Triangle

Here we will prove that the equal sides YX and ZX of an isosceles triangle XYZ are produced beyond the vertex X to the points P and Q such that XP is equal to XQ. QY and PZ are joined. Show that QY is equal to PZ.


In ∆XYZ, XY = XZ. YX and XZ are produced to P and Q respectively such that XP = XQ. Q, Y and P, Z are joined.

Theorem on Isosceles Triangle

To prove: QY = PZ.



1. In ∆XQY and ∆XPZ,

(i) XY = XZ.

(ii) XQ = XP.

(iii) ∠QXY = ∠PXZ.


2. ∆XQY ≅ ∆XPZ.

3. QY = PZ. (Proved)



(i) Given.

(ii) Given.

(iii) Vertically opposite angles.


2. By SAS criterion.


9th Grade Math

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