✧Answer:

1.A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.

2.A Inequalities is a relation which makes a non-equal comparison between two numbthe theorem and its converse are writters or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

3.A Theorem is a non-self-evident statement that has been proven to be true, either on the basis of generally accepted statements such as axioms or on the basis of previously established statements such as other theorems.

4.A 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.

5.The Theorem and its converse are written as the SAS Inequality Theorem and the SSS Inequality Theorem respectively.

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Define the following:

1. Triangle

2. Inequalities

3. Theorem

4. Hinge Theorem

5. Converse of Hinge Theorem

1.A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

2.In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

3.A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments. In general, a theorem is an embodiment of some general principle that makes it part of a larger theory. The process of showing a theorem to be correct is called a proof.

4.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.

5.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.