In any triangle, the greater side and greater angle are opposite to one another. If two sides are not the same the angle opposite to the longer side will be greater. The side opposite to the greatest angle in a triangle is the longest. In the below section we have proven that Greater Side has the Greater Angle Opposite to its inequalities in triangles.
Greater Angle has the Greater Side Opposite to It Theorem
Question: In a triangle prove that the greater angle has the longer side opposite to it
Theorem: If in a triangle two angles are unequal, then the side opposite to the greater angle is longer than the side opposite to the smaller angle.
let ABC be a triangle in which the angle ABC is greater than the angle ACB.
To prove that:
AC > AB
let us try to prove this by contradiction. let us assume that AC is not longer than AB.
case I : AC = AB
case II : AC < AB
If in case AC = AB. triangle ABC would have been isosceles triangle and angle ABC = angle BAC
” If in a triangle two sides are unequal, then angle opposite to longer side is greater than the angle opposite to shorter side”.
Thus the only remaining possibility is that the side AC is longer than the side BC.
Therefore AC > AB
Thus it is proven that Greater Angle has the Greater Side Opposite to It.
Read Similar: Greater Side has the Greater Angle Opposite to It
FAQs on Greater Angle has the Greater Side Opposite to It
1. What is the relationship between the largest angle of a triangle and the side opposite it?
In a triangle, the greater side and greater angle are opposite one another. In any triangle, the smallest side and smallest angle are opposite one another.
2. How can you tell which angle is greater in a triangle?
If one side of a triangle is longer than another side, then the angle opposite the longer side will be larger than the angle opposite the shorter side.
3. How does the triangle inequality theorem relate to angles?
In triangle inequality theorem holds that the longer side of the triangle will stand opposite the larger angle and that the larger angle will stand opposite the longer side.