Arithmetic
Arithmetic Progression
Associative Property
Averages
Brackets
Closure Property
Commutative Property
Conversion of Measurement Units
Cube Root
Decimal
Divisibility Principles
Equality
Exponents
Factors
Fractions
Fundamental Operations
H.C.F / G.C.D
Integers
L.C.M
Multiples
Multiplicative Identity
Multiplicative Inverse
Numbers
Percentages
Profit and Loss
Ratio and Proportion
Simple Interest
Square Root
Unitary Method
Algebra
Cartesian System
Order Relation
Polynomials
Probability
Standard Identities & their applications
Transpose
Geometry
Basic Geometrical Terms
Circle
Curves
Angles
Define Line, Line Segment and Rays
Non-Collinear Points
Parallelogram
Rectangle
Rhombus
Square
Three dimensional object
Trapezium
Triangle
Trigonometry
Trigonometry Ratios
Data-Handling
Arithmetic Mean
Frequency Distribution Table
Graphs
Median
Mode
Range

Videos
Solved Problems
Home >> Triangle >> Properties >> Angles opposite to equal sides of triangle are equal >>

## 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

Copyright@2022 Algebraden.com (Math, Algebra & Geometry tutorials for school and home education)