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Hinge theorem. 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 ...
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]
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: If two triangles have two sides equal to two sides, but have one of the angles contained by the equal straight lines greater than the other, they will also have the base ...
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 longer the length of the remaining side.
(Redirected from Hinge theorem) The Base Angle Theorem states that in an isosceles triangle, the angles opposite the congruent sides are congruent. Proof. Since the triangle only has three sides, the two congruent sides must be adjacent. Let them meet at vertex . Now we draw altitude to .
Hinge Th. m. If two sides of a 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.
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^'.
Proving the Hinge Theorem (also known as the Alligator theorem) two ways, which rely on the triangle inequality theorem or its converse.
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.
Theorem. If two triangles have two pairs of sides which are the same length, the triangle in which the third side is longer also has the larger angle contained by the first two sides. In the words of Euclid:
Math texts, online classes, and more for students in grades 5-12. Visit AoPS Online ‚. Books for Grades 5-12 Online Courses
John Newton proved the hinge theorem. Does that make it reliable? Squall BL The FMA just released an expansion of the Hinge Theorem on spp15.emagc.com. Click on the "Daily Rabble" tab to see the more reliable info. This information is groundbreaking, and it may merit an article for the hinge theorem. Squall BL 22:16, 28 May 2010 (UTC)
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
In geometry, the hinge 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.
I came across the Hinge Theorem and I want to see if it can be generalized to non-Euclidean metrics. It's page on Wikipedia states that "The hinge theorem holds in Euclidean spaces and more generally in simply connected non-positively curved space forms." However, no reference is given.
A hinge is a mechanical bearing that connects two solid objects, typically allowing only a limited angle of rotation between them. Two objects connected by an ideal hinge rotate relative to each other about a fixed axis of rotation, with all other translations or rotations prevented; thus a hinge has one degree of freedom.
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.
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. This theorem is given as Proposition 24 in Book I of ...
Triangle Inequality In Two Triangles: The Hinge Theorem or SAS Inequality Theorem [ edit | edit source ] If two sides of one triangle are congruent to two sides of a second triangle, and the angle between these sides of the first triangle is greater than the angle between these side of the second, then the third side of the first triangle is ...