Triangles class 9 Introduction 2
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In an isosceles triangle where two sides are equal, the angles opposite the equal sides are also equal. The proof constructs a bisector of one angle to intersect the base of the triangle, forming two smaller triangles. Since the smaller triangles have two equal sides and an included angle, they are congruent by the Side-Angle-Side rule. Therefore, the angles opposite the equal sides of the original triangle are equal.
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Triangles class 9 Introduction 2
- 1. Theorem : Angles opposite to equal sides of an isosceles triangle are equal. PROOF- GIVEN: In isosceles Triangle ABC, AB=BC TO PROVE:∠𝑩 = ∠𝑪 CONSTRUCTION-Let us draw the bisector of ∠ A and let D be the point of intersection of this bisector of ∠ A and BC PROOF-In Δ BAD and Δ CAD, AB = AC (Given) ∠BAD = ∠CAD (By construction) AD = AD (Common) So, Δ BAD ≅ Δ CAD (By SAS rule) So, ∠ABD = ∠ACD, since they are corresponding angles of congruent triangles. So, ∠B = ∠C