Question

Verify experimentally that the opposite angles of equal sides of an
isosceles triangle are equal.

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Answer 1

Angles Opposite to Equal Sides of an Isosceles Triangle are Equal

 Here we will prove that in an isosceles triangle, the angles opposite to the equal sides are equal.

Solution:

Angles Opposite to Equal Sides of an Isosceles Triangle are Equal

Given: In the isosceles ∆XYZ, XY = XZ.

To prove: ∠XYZ = ∠XZY.

Construction: Draw a line XM such that it bisects ∠YXZ and meets the side YZ at M.

Proof:

1. In ∆XYM and ∆XZM,

XY = XZ (Given)

XM = XM  (Common side)

∠YXM = ∠ZXM  (XM bisects ∠YXZ. )

∆XYM ≅ ∆XZM ( By SAS criterion )

∠XYZ = ∠XZY (CPCTC)

Hence Proved.

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