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14 Cards in this Set
- Front
- Back
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Congruent Triangles
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Two triangles are congruent if and only if, for some correspondence between the two triangles, each pair of correspongding sides are congruent and each pair of corresponding angles are congruent.
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SSS - The Side-Side-Side Postulate
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Given a correspondence between two triangles, if three sides of one triangle are congruent to the corresponding three sides of the second triangle, then the two triangles are congruent.
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SAS - The Side-Angle-Side Postulate
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Given a correspondence between two triangles, if two sides and the included angle of one triangle are congruent to the correspoinding two sides and the included angle of the second triangle, then the two triangles are congruent.
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ASA - The Angle-Side-Angle Postulate
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Given a correspondence between two triangles, if two angles, and the included side of one triangle are congruent to the corresponding two angles and the included side of the second triangle, then the two triangle are congruent.
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AAS - The Angle-Angle-Side Theorem
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Given a correspondence between two right triangles, if the hypotenuse and an acute angle of one triangle are congruent to the corresponding hypotenuse and acute angle of the second triangle, then the two triangles are congruent.
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HL - The Hypotenuse-Leg Theorem
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Given a correspondence between two right triangles, if the hypotenuse and a leg of one triangle are congruent to the corresponding hypotenuse and leg of the second triangle, then the two triangles are congruent.
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Similar Triangles
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Two triangles are similar if and only if, for some correspondence between the two triangles, each pair of corresponding angles are congruent and the ratios of corresponding sides are equal.
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AA Similarity Postulate
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If two angles of one triangle are congruent, respectively, to two angles of another triangle, then the two triangles are similar.
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Right Triangle Similarity Theorem
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If an acute angle of one right triangle is congruent to an acute angle of another right triangle, then the triangles are similar.
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SAS Similarity Theorem
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If an angle of one triangle is congruent to an angle of another triangle, and if the lengths of the sides including these angles are proportional, then the triangles are similar.
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SSS Similarity Theorem
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If the corresponding sides of two triangles are proportional, then the two triangles are similar.
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The Pythagorean Theorem
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In a right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs. When the lengths of the legs are a and b, and the length of the hypotenuse is c, then a squared + b squared, = c squared.
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The 45º-45º-90º Triangle Relationship Theorem
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The length of the hypotenuse of any 45º-45º-90º triangle is the length of a leg times the sq.rt. of 2.
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The 30º-60º-90º Triangle Relationship Theorem
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The length of the hypotenuse of any 30º-60º-90º triangle is two times the length of the shorter leg. The length of the longer leg is the length of the shorter leg times the sq.rt. of 2.
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