Geometry - Loudoun County Public Schools.
Learn what it means for two figures to be similar, and how to determine whether two figures are similar or not. Use this concept to prove geometric theorems and solve some problems with polygons.Similarity Statements in Geometry: A similarity statement in geometry comes in handy when encountering two shapes, such as equilateral triangles that look the same but are of different sizes.Congruence means two objects (whether two dimensional or three dimensional) are identical in size and shape. Everything about them -- their angles, lengths of sides, overall dimensions -- are identical. Similar figures have the same shape and proportions but are not necessarily the same size. Table Of Contents. Congruence; Try It! Geometry Try.
Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection. This means that either object can be rescaled, repositioned, and reflected, so as to coincide.When it comes to the study of geometry, precision and specificity is key. It should come as no surprise, then, that determining whether or not two items are the same shape and size is crucial. Congruence statements express the fact that two figures have the same size and shape.
Similarity of triangles (EMCJG) To prove two polygons are similar, we need to show that two conditions are true: (a) all pairs of corresponding angles are equal and (b) all pairs of corresponding sides are in the same proportion. To prove two triangles are similar, we need only show that one of the conditions is true.
