First Known Use of congruent 15th century, in the meaning defined at sense 1. History and Etymology for congruent Middle English, from Latin congruent-, congruens , present participle of congruere — see congruous. Learn More About congruent. Time Traveler for congruent The first known use of congruent was in the 15th century See more words from the same century. Style: MLA. Kids Definition of congruent. Get Word of the Day daily email! Test Your Vocabulary. Can you spell these 10 commonly misspelled words?
Love words? Need even more definitions? Just between us: it's complicated. More formally, two sets of points are called congruent , if and only if one can be transformed into the other by isometry. For isometry, rigid motions are used. This means that two geometrical figures are congruent if one object can be repositioned, rotated or reflected—but not resized—so that it coincides exactly with the other object.
If one of the object has to change its size, then the two objects are not congruent: they are just called similar. As an example, two distinct plane figures on a piece of paper are congruent if we can cut them out and then match them up completely turning the paper over here is permitted. The shapes still have congruent angles, but the line segments that make up the card are now different lengths, so the two shapes are no longer congruent. Dilating one of two congruent shapes creates similar figures , but it prevents congruency.
Figures are similar if they are the same shape; the ratios and length of their corresponding sides are equal. So, are congruent figures similar? Technically, yes, all congruent figures are also similar shapes. But not all similar shapes have congruency. In geometry, similar triangles are important, and three theorems help mathematicians prove if triangles are similar or congruent.
Usually, we reserve congruence for two-dimensional figures, but three-dimensional figures, like our chess pieces, can be congruent, too. Think of all the pawns on a chessboard. They are all congruent. The geometric figures themselves do not matter. You could be working with congruent triangles, quadrilaterals, or even asymmetrical shapes. Here are two congruent figures:. To summarize, congruent figures are identical in size and shape; the side lengths and angles are the same.
They can be rotated, reflected, or translated, and still be congruent. They cannot be dilated enlarged or shrunk and be congruent. Angle Relationships. Get better grades with tutoring from top-rated professional tutors. Get help fast. Want to see the math tutors near you?
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