Similarity and Congruence

1192 WordsJul 5, 20135 Pages
Similarity and congruence Two triangles are said to be similar if every angle of one triangle has the same measure as the corresponding angle in the other triangle. The corresponding sides of similar triangles have lengths that are in the same proportion, and this property is also sufficient to establish similarity. A few basic theorems about similar triangles: * If two corresponding internal angles of two triangles have the same measure, the triangles are similar. * If two corresponding sides of two triangles are in proportion, and their included angles have the same measure, then the triangles are similar. (The included angle for any two sides of a polygon is the internal angle between those two sides.) * If three…show more content…
Theorem 5-9. SSS Similarity Theorem If all three pairs of corresponding sides of two triangles are proportional, then the two triangles are similar. Transversal In geometry, a transversal is a line that passes through two lines in the same plane at different points. When the lines are parallel, as is often the case, a transversal produces several congruent and several supplementary angles. When three lines in general position that form a triangle are cut by a transversal, the lengths of the six resulting segments satisfy Menelaus' theorem. The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side. In mathematics, the Pythagorean theorem — or Pythagoras' theorem — is a relation inEuclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas, it states: In any right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle). The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation: where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides. The