Sides Opposite to the Equal Angles of a Triangle are Equal
Here we will prove that the sides opposite to the equal angles of a triangle are equal.
Given: In ∆ABC, ∠XYZ = ∠XZY.
To prove: XY = XZ.
Construction: Draw the bisector XM of ∠YXZ so that it meets YZ at M.
Proof:
|
Statement 1. In ∆XYM and ∆XZM, (i) ∠XYM = XZM (ii) ∠YXM = ∠ZXM (iii) XM = XM. 2. ∆XYM ≅ ∆XZM 3. XY = XZ. (Proved) |
Reason 1. (i) Given. (ii) XM bisects ∠YXZ. (iii) Common side. 2. By AAS criterion. 3. CPCTC. |
From Sides Opposite to the Equal Angles of a Triangle are Equal to HOME PAGE
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.
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.