Greater Side has the Greater Angle Opposite to It can also be called If two sides of a triangle are unequal, then the angle opposite to it is greater. It is the theorem from the Inequalities in Triangles. To prove Greater Side has the Greater Angle Opposite to It first you have to write the theorem clearly. If the two sides of a triangle are not equal, then the angle opposite to the greater side is greater. Scroll down this page to know how to prove the inequalities in triangles theorem “Greater Side has the Greater Angle Opposite to It.”
Greater Side has the Greater Angle Opposite to It Theorem
Given theorem
Greater Side has the Greater Angle Opposite to It
Let us assume In ∆ABC, AC > AB (AC is greater than AB)
To Prove:
∠ABC >∠ACB
From AC, cutoff AP such that AP equals AB join C and P
Proof
In ∆ABP, ∠ACP = ∠APC [ AC = AP]……equation 1
∠ACP = x°
∠PCB = y°
∠APC = x°
∠APC = ∠ACP + ∠CPB [ therefore in the triangle BPC exterior ∠APB = sum of interior opposite angles ∠PCB = ∠ACB and ∠PBC].. equation 2
Therefore ∠APC > ∠ACP (equation 3)….. from equation 2
Therefore ∠APC > ∠ACP (equation 4)… using equation 1 and equation 2
But ∠ACP > ∠ABP [ ∠APC = ∠ACP + ∠CPB]…. equation 5
Therefore ∠ABC >∠ACB [ using equation 5 and 4]
Hence it is proven that Greater Side has the Greater Angle Opposite to It.
FAQs on Greater Side have the Greater Angle Opposite to It
1. Is the angle opposite to the greater side greater?
If two sides of a triangle are not the same, the angle opposite to the longer side is larger.
2. Which angle is the bigger angle opposite of shorter side or angle opposite of longer side?
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. What angle is opposite the shortest side?
The shortest side is always opposite the smallest interior angle. The longest side is always opposite the largest interior angle.