How do you prove that if two sides of a triangle are unequal the angle opposite to the longer side is larger?

If two sides of a triangle are unequal, the angle opposite to the longer side is larger (or greater). You may prove this theorem by taking a point P on BC such that CA = CP.

How do you prove one angle is bigger than another in a triangle?

The SAS Inequality Theorem (Hinge Theorem): If two sides of a triangle are congruent to two sides of another triangle, but the included angle of one triangle has greater measure than the included angle of the other triangle, then the third side of the first triangle is longer than the third side of the second triangle.

How does triangle inequality theorem relate to angles?

Theorem 36: If two sides of a triangle are unequal, then the measures of the angles opposite these sides are unequal, and the greater angle is opposite the greater side.

Which theorem states that when a triangle having unequal sides the side is the longest if the side is opposite to the largest angle?

The longest side in a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle. Triangle Inequality: In any triangle, the sum of the lengths of any two sides is greater than the length of the third side. Pythagorean Theorem: In a right triangle with hypotenuse . c , a 2 + b 2 = c 2 .

Are two sides of a triangle equal?

An isosceles triangle therefore has both two equal sides and two equal angles. A triangle with all sides equal is called an equilateral triangle, and a triangle with no sides equal is called a scalene triangle.

What is Triangle Inequality theorem 1?

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

What is triangle inequality theorem 2?

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side. In other words, as soon as you know that the sum of 2 sides is less than (or equal to) the measure of a third side, then you know that the sides do not make up a triangle.

What is triangle inequality theorem 3?