Inequalities

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Step 1: Use the side-angle relationship in a triangle. Step 2: The greater side has the greater angle opposite to it. Step 3: Since AB > AC, the angle opposite AB is greater than the angle opposite AC…

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Step 1: Use the converse relationship between angles and opposite sides. Step 2: The greater angle has the greater side opposite to it. Step 3: angle CAB is greater than angle B, so the side opposite …

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In a triangle, side length and opposite angle are linked. If one side is longer, the angle opposite it opens wider. For triangle ABC, if AB > AC, then angle ACB > angle B. This helps compare sides qui…

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Theorem 3 starts with unequal sides and concludes unequal opposite angles. Theorem 4 starts with unequal angles and concludes unequal opposite sides. That reversed logic makes it the converse. Example…

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Step 1: In a triangle, the side opposite the greater angle is greater. Step 2: If angle A is greatest in triangle ABD, then the side opposite it is the greatest side. Step 3: The descending order is A…

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Use it when comparing distances from an external point to different points on a line. Example setup: point O outside line AB, OP perpendicular to AB, and OQ joins O to another point Q on AB. Then OQ >…

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Step 1: In triangle OPQ, OP is perpendicular to AB, so angle OPQ is a right angle. Step 2: In a right triangle, the right angle is the greatest angle. Step 3: The side opposite the greater angle is gr…

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Corollary 1: AB+AC>BC; AB+BC>AC; BC+AC>AB. Here AB, BC, and AC are the sides of triangle ABC. Example: if AB and AC are known, their sum must be greater than BC. This helps check whether three lengths…