In geometry, the hinge theorem (sometimes called the open mouth theorem) states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle. [1]

Apr 18, 2023 · Hinge theorem is a theorem that compares two triangles and states that if two sides of both triangles are equal, then the length/measure of the third side will depend upon the measure of the interior angle. The higher the interior angle, the …

This theorem is called the "Hinge Theorem" because it acts on the principle of the two sides described in the triangle as being "hinged" at their common vertex. Consider the alligator jaws at the right.

Directions: Grab a paper and pencil to make your computations. 1. Which of the following choices is a possible length for the segment from A to B? 2. Given the diagram at the right, what can be concluded regarding AB and AC? No conclusion can be made. 3. Given the diagram at the right, what can be concluded regarding m∠U and m∠E?

The Hinge 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 greater than the included angle of the second triangle, then the third side of the first triangle is greater

Oct 18, 2023 · Theorem. If two triangles have two pairs of sides which are the same length, the triangle with the larger included angle also has the larger third side. In the words of Euclid:

The Hinge Theorem helps you compare side measurements of two triangles when you have two sets of congruent sides. Follow along with this tutorial to see this theorem used to find the relationship between the sides of two triangles.

Mar 5, 2025 · The hinge theorem says that if two triangles DeltaABC and DeltaA^'B^'C^' have congruent sides AB=A^'B^' and AC=A^'C^' and ∠A>∠A^', then BC>B^'C^'.

The Hinge Theorem This is one of several inequality theorems for triangles. Theorem. Given triangles ABC and ABD which satisfy |AC| = |AD|, then we have |BC| < |BD| if and only if |∠∠∠∠CAB| < |∠∠∠∠DAB|. This result, which can be proved using the Law of Cosines from trigonometry c2 2= a + b2 – 2ab cos |∠∠∠∠ACB|

The hinge theorem states that when two sides of two triangles are congruent and the angle between is smaller for one, then the third side of that triangle will be shorter than the other's.