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Axioms Corollaries
Axioms Corollaries

Congruency and Similarity
Congruency and Similarity

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Similar Right Triangles

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Printable PDF

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Numbers & Geometry - Muskingum University

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... A and B are on the edges of a ravine. What is AB? One angle pair is congruent, because they are vertical angles. Two pairs of sides are congruent, because their lengths are equal. Therefore the two triangles are congruent by SAS. By CPCTC, the third side pair is congruent, so AB = 18 mi. Holt McDoug ...
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... 5-6 Inequalities in 2 Triangles Inequalities in 2 Hinge Theorem Triangles If 2 sides of 1 triangle are congruent to 2 sides of another triangle and the included angles are not congruent, then the longer side is across from the larger included angle. Converse of the Hinge Theorem If 2 sides of a tria ...
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Integer triangle

An integer triangle or integral triangle is a triangle all of whose sides have lengths that are integers. A rational triangle can be defined as one having all sides with rational length; any such rational triangle can be integrally rescaled (can have all sides multiplied by the same integer, namely a common multiple of their denominators) to obtain an integer triangle, so there is no substantive difference between integer triangles and rational triangles in this sense. Note however, that other definitions of the term ""rational triangle"" also exist: In 1914 Carmichael used the term in the sense that we today use the term Heronian triangle; Somos uses it to refer to triangles whose ratios of sides are rational; Conway and Guy define a rational triangle as one with rational sides and rational angles measured in degrees—in which case the only rational triangle is the rational-sided equilateral triangle.There are various general properties for an integer triangle, given in the first section below. All other sections refer to classes of integer triangles with specific properties.
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