Angle-angle-angle (AAA) similarity
The angle-angle-angle (AAA) similarity test states that given two triangles that have corresponding angles that are congruent, then the triangles are similar. As we know the sum of the interior angles in a triangle is 180°, so if two corresponding are congruent, then the other ones should be as well.
A statement assumed to be true without proof.
A sequence of justified conclusions used to prove the validity of an if-then statement.
Side-angle-side (SAS) similarity
The side-angle-side (SAS) similarity test states that given two triangles that have two pairs of sides that are proportional and the included angles are congruent, then the triangles should be similar.
Side-side-side (SSS) similarity
The side-side-side (SSS) similarity test states that for two triangles to be similar; all corresponding sides should be proportional.
two polygons are similar polygons if corresponding angles have the same measure and corresponding sides are in proportion.
Similar triangles are triangles which have the same shape but probably different size. Corresponding angles need to be congruent, and corresponding sides are in proportion.
A theorem in mathematics is a proven fact. A theorem about polygon must be true for every polygon; there can be no exceptions. An idea which works in several different cases is not enough.
Interactive Geometric Applets: Relevant Theorems.
Two parallel lines that are cut by a transversal have all acute angles
congruent, and all obtuse angles congruent. If you take one acute, and
one obtuse; their sum is 180°. In other words angle pairs like corresponding,
alternate interior, and alternate exterior angles are congruent, an consecutive interior
angles are supplementary.
You may drag point "B" in this applet to verify all these angle relationships.
Supplementary angles are two positive angles whose sum is 180°.
Drag point "C" within the shaded area to verify that you have
supplementary angles. Check the sum below the figure.
Congruent Supplements Theorem states that given two angles supplementary to the
same angle, then they are congruent between them.
Vertical Angles are a pair of nonadjacent angles formed by two straight lines like in the applet below.
Move point "C" right and left, and see how the vertical pairs remain congruent.
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