What is the SAS Inequality theorem?
What is the SAS Inequality theorem?
The SAS Inequality Theorem states: If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first triangle is larger than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle.
How do you prove the angle of an inequality?
Hence proved that the exterior angle of a triangle is equal to the sum of the two opposite interior angles….Proof of Exterior Angle Theorem.
| Statement | Reason |
|---|---|
| ∠a + ∠b = ∠x + ∠y | From the above statements |
| ∠ACD = ∠x + ∠y | From the construction of CE |
How do you prove the Hinge Theorem?
To prove the Hinge Theorem, we need to show that one line segment is larger than another. Both lines are also sides in a triangle. This guides us to use one of the triangle inequalities which provide a relationship between sides of a triangle. One of these is the converse of the scalene triangle Inequality.
What is triangle inequality theorem 3?
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
What is converse of hinge?
The converse of the hinge theorem is also true: If the two sides of one triangle are congruent to two sides of another triangle, and the third side of the first triangle is greater than the third side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second …
Why is exterior angle theorem true?
The exterior angle theorem is Proposition 1.16 in Euclid’s Elements, which states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles. This is a fundamental result in absolute geometry because its proof does not depend upon the parallel postulate.
What is exterior angle Inequality theorem?
The exterior angle inequality theorem states that the measure of any exterior angle of a triangle is greater than both of the non-adjacent interior angles.
