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.

Solution:

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.

Proof:

          Statement

1. In ∆XQY and ∆XPZ,

(i) XY = XZ.

(ii) XQ = XP.

(iii) ∠QXY = ∠PXZ.

 

2. ∆XQY ≅ ∆XPZ.

3. QY = PZ. (Proved)

Reason

1.

(i) Given.

(ii) Given.

(iii) Vertically opposite angles.

 

2. By SAS criterion.

3. CPCTC.












9th Grade Math

From Theorem on Isosceles Triangle to HOME PAGE


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?