Answer to Question #206925 in Geometry for lele

Question

suggest a sequence of statements that logically prove that the angles opposite the congruent sides of an isosceles triangle are equal in size. explain each statement simply and clearly. use illustrations to enhance your explanation

Answer 1

Isosceles Triangle Theorem states:

If two sides of a triangle are congruent, then angles opposite those sides are congruent.

THEOREM PROOF :

Consider an isosceles triangle PQR where PR=QR . We need to prove that the angles opposite to the sides PR and QR are equal , that is ∠RPQ = ∠RQP

We first draw a bisector of ∠PRQ and named it RS.

Now in ∆PRS and ∆QRS , we have

PR = QR (given)

∠PRS = ∠QRS (by construction)

CD = CD (common to both)

Thus, ∆PRS ≅ ∆QRS (by SAS congruency)

So, ∠RPQ = ∠RQP (by CPCTC)

where SAS= (side-angle-side)

and CPCTC = (Corresponding parts of congruent triangles are congruent)

HENCE PROVED .