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.
Furthermore, how do you prove converse hinge Theorem?
Converse of the Hinge Theorem :
If two sides of one triangle are congruent to two sides of another triangle, and the third side of the first is longer than the third side of the second, then the included angle of the first is larger than the included angle of the second.
Also to know is, what are hinge angles?
What are the two hinge theorems?
One of these is the converse of the scalene triangle Inequality. This tells us that the side facing the larger angle is larger than the side facing the smaller angle. The other is the triangle inequality theorem, which tells us the sum of any two sides of a triangle is larger than the third side.
What is converse Pythagorean Theorem?
The converse of the Pythagorean Theorem says that if a triangle has sides of length a, b, and c and if a^2 + b^2 = c^2 then the angle opposite the side of length c is a right angle.
What is hinge theorem and its converse?
The converse of the hinge theorem states that if two triangles have two congruent sides, then the triangle with the longer third side will have a larger angle opposite that third side.
What is the difference between Hinge Theorem and converse of Hinge Theorem?
The SSS inequality theorem is the converse of the hinge theorem: if two sides of two triangles are congruent, but the third side on one is shorter than on the other, we know that the corresponding angle is also smaller.
What is the hinge theorem in geometry?
Geometry. The Hinge Theorem states that if two sides of two triangles are congruent and the included angle is different, then the angle that is larger is opposite the longer side.
Which statement correctly describes the hinge Theorem?
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.
Why folder is a Hinge Theorem?
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. … (May also be referred to as the SSS Inequality Theorem.) … We have seen how inequalities can be applied to the sides and angles of a single triangle. …
Why is it called the Hinge Theorem?
the vertex of the angle acts like a hinge to open the triangle. it’s named after Joseph Hinge, the man who discovered it.
Why scissor is a hinge Theorem?
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.