Math Quiz

• An exterior angle of a triangle is an angle that forms a linear pair with one of the angles of the triangle. Remote interior angles of triangle are the angles that do not form a linear pair with the exterior angle.


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• Exterior Angle Inequality Theorem • For any triangle, the measure of an exterior angle is equal to the sum of the measures of its two remote interior angles.
• • The measure of an exterior angle of a triangle is greater than the measure of either of its two remote interior angles.


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• Triangle Inequality Theorem The sum of any two side lengths of a triangle is greater than the third side length.
• Triangle Inequality- It states that the sum of the lengths of any two sides of a angle is greater than the length of the remaining side. It follows from the fact that a craight line is the shortest path between two points. The inequality is strict if the triangle - non-degenerate (meaning it has a non-zero area
• CONVERSE OF THE HINGE THEOREM If two sides of a 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 in the first triangle is greater than the included angle in the second triangle
• HINGE THEOREM 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
• Theorem 1 (Ss Aa) If one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side.
• 2. Theorem 2 (Aa Ss) If one angle of a triangle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle.
• 3. Theorem 3 (S1 + S2 >S3) The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
• 4.Exterior Angle Inequality Theorem The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle
• 5. Hinge Theorem or SAS Inequality Theorem If two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is greater than the included angle of the second, then the third side of the first triangle is longer than the third side of the second.
• 6.Converse of Hinge Theorem or SSS Inequality Theorem If two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second, then the included angle of the first triangle is larger than the included angle of the second.