Students should be familiar with geometric markings in figures to indicate congruence of sides and angles and to indicate parallel sides. An equal number of hatch (hash) marks indicate that those sides are equal in length. An equal number of arrows indicate that those sides are parallel. An equal number of angle curves indicate that those angles have the same measure. See the diagram below. [Graphic cannot be reproduced.]
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Parallelograms, with the exception of rectangles and rhombi, have no lines of symmetry. A rectangle and a rhombus have two lines of symmetry, with the exception of a square which has four lines of symmetry.
Similarity statements can be used to determine corresponding parts of similar figures such as: Given: ΔABC ~ ΔDEF; ∠A corresponds to ∠D; Line Segment AB corresponds to Line Segment DE.
The symbol ~ is used to represent similarity.
How do polygons that are similar compare to polygons that are congruent? Congruent polygons have the same size and shape. Similar polygons have the same shape, and corresponding angles between the similar figures are congruent. However, the lengths of the corresponding sides are proportional. All congruent polygons are considered similar with the ratio of the corresponding sides being 1:1.
Identify corresponding sides and corresponding and congruent angles of similar figures using the traditional notation of curved lines for the angles.