For example, rectangle ABCD and rectangle PQRS are. Refer to congruent triangles to see the methods of determining the congruence of triangles. If two figures have the same shape and the same size, then they are said to be congruent figures. Two circles are congruent if their radii, diameters, areas, or their circumferences are equal.Two squares are congruent if their sides are equal, perimeters, or areas are equal.Proving congruence differs for different shapes. Congruent shapes Two shapes that are the same size and the same shape are congruent. However, it is usually not necessary to know that every part is equal in order to prove congruence. Two figures are congruent if their corresponding parts are congruent. If quadrilateral ABCD is reflected across the red line below to quadrilateral ABCD', then, ABCD ≅ ABCD' since both triangles have the same size and shape. If quadrilateral ABCD is rotated clockwise to quadrilateral ABCD', then, ABCD ≅ ABCD' since both quadrilateral have the same size and shape. If quadrilateral ABCD is translated diagonally to quadrilateral ABCD' then, quadrilateral ABCD ≅ quadrilateral ABCD' since both quadrilaterals have the same size and shape. There are three transformations that produce congruent figures. ![]() There are many types of figures the following are just 2 examples.įor the two congruent triangles above, the following angles and sides are congruent: ∠A≅∠D, ∠B≅∠E, ∠C≅∠F AB≅DE, BC≅EF, AC≅DF.įor the two congruent circles above, the radius, area, and circumference are equal in value. ![]() When two figures are congruent, their corresponding parts are equal in value including side, edge, angles, faces, area, volume, and more. Tick marks (like those used with congruent line segments) can also be used along with arcs, as shown in the figure below. In order for two shapes to be congruent, each must have the same amount of sides and their angles must also be the same. ![]() Two angles are said to be congruent if they are of equal measure. Any two line segments are said to be congruent if they are equal in length. Congruence can be applied to line segments, angles, and figures. ∠A and ∠B have a measure of 60°, so ∠A≅∠B.Ĭongruent angles can also be denoted by placing an equal number of arcs between the rays that form the congruent angles. Congruent shapes are two shapes that are equal in shape and size. In geometry, congruent means identical in shape and size.
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