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 that two ratios are equal.
One of four numbers that form a true proportion.
Pythagorean theorem a2 + b2 = c2.
The Pythagorean theorem states that if you have a right triangle, then the square built on the hypotenuse is equal to the sum of the squares built on the other two sides.
A quotient of 2 numbers.
A triangle that has a 90 degree angle.
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 polygon with three sides.
Interactive Geometric Applets: Relevant Theorems.
This great applet shows you, how you may draw three similar triangles, after you
draw the altitude from the hypotenuse to the right angle in a right triangle.
The triangles have been drawn with the same orientation. You may identify them
by the colors, the labels in the vertices, and the colors and measures of the side segments.
Drag point "B" to see how they update angles and side lengths to keep their
proportionality and similarity as shown in the provided extended proportions.
Vocabulary Puzzle Interactive
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