Angles opposite to equal sides of a triangle are equal

Sum of Two Sides	Angle Sum Property	Angles opposite to equal sides of triangle are equal	Angle opposite to longer side is greater	Pythagoras Theorem
Exterior Angle Property of a Triangle	Mid point property of Triangle	Triangles on same base & between same parallel lines

Before you study this property of a triangle, you are advised to read: What are Congruent Triangles ? In the below diagram, we have a Triangle ABC which have two equal sides i.e. AC and BC (as highlighted by pink line) Now, Angle opposite to side AC is Angle B (as shown below): And Angle opposite to side BC is Angle A (as shown below): Side AC = Side BC (given) And as explained in the above diagrams: Angle opposite to side AC is Angle B and Angle opposite to side BC is Angle A So, as per the given property, which says that Angles opposite to equal sides of a triangle are equal , we can conclude that: Angle B = Angle A How this property is obtained: In the below diagram, we have a Triangle ABC which have two equal sides i.e. AC and BC (as highlighted by pink line) Now, draw the bisector of Angle C, which meets side AB at D (as shown below): Now, let's prove △ ADC ≅ △ BDC In △ ADC and △ BDC: AC = BC (given) Angle ACD = Angle BCD (by construction of bisector) CD = CD (common sides) So, by SAS rule of congruency, it proved that △ ADC ≅ △ BDC And since corresponding angles of congruent triangles are also equal, so we get: Angle DAC = Angle DBC Or we can also write it as: Angle A (Angle opposite to side BC) = Angle B (angle opposite to side AC) Hence, this proves the property of triangle : Angles opposite to equal sides of a triangle are equal