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.
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.
Interactive Geometric Applets: Relevant Theorems.
An enlargement is when you multiply by a scale factor all the dimensions of a given
figure; whereas that a reduction requires that you divide by the scale factor. The resulting
figures are similar figures, because they have the same shape but different size.
This applet will enable you to visualize this relationship of similarity between two
Parallel lines cut by transversals form proportional segments.
Verify that this is true by dragging point "E" in this applet.
Pay attention to the proportion see how it updates values as you drag the point.
The Basic Proportionality Theorem states that if you have a segment
connecting two sides of a triangle, and parallel to the third side; then
the segments formed are proportional.
Prove this theorem by dragging any point in the below figure.
Look at the proportion written below, it changes as you move the points.
The Triangle Midsegment Theorem states that if you have a segment joining two sides of the triangle by the midpoint,
then the third side is parallel to this segment, and measures twice the length of the midsegment.
Drag in this figure any of the vertices and verify these relationships.
Vocabulary Puzzle Interactive
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