翻訳と辞書 Words near each other ・ Congridae ・ Congrier ・ Congrinae ・ Congriscus ・ Congriscus maldivensis ・ Congriscus marquesaensis ・ Congriscus megastomus ・ Congro Volcanic Fissural System ・ Congrogadus subducens ・ Congrosoma evermanni ・ Congrove Field and The Tumps ・ Congrua ・ Congrua portio ・ Congruence ・ Congruence (general relativity) ・ Congruence (geometry) ・ Congruence (manifolds) ・ Congruence bias ・ Congruence coefficient ・ Congruence ideal ・ Congruence lattice problem ・ Congruence of squares ・ Congruence of triangles ・ Congruence principle ・ Congruence relation ・ Congruence subgroup ・ Congruence-permutable algebra ・ Congruent isoscelizers point ・ Congruent melting ・ Congruent number Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Congruence (geometry) ： ウィキペディア英語版 In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. So 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 is permitted.In elementary geometry the word ''congruent'' is often used as follows. The word ''equal'' is often used in place of ''congruent'' for these objects.*Two line segments are congruent if they have the same length. *Two angles are congruent if they have the same measure.*Two circles are congruent if they have the same diameter.In this sense, ''two plane figures are congruent'' implies that their corresponding characteristics are "congruent" or "equal" including not just their corresponding sides and angles, but also their corresponding diagonals, perimeters and areas.The related concept of similarity applies if the objects differ in size but not in shape.==Determining congruence of polygons==For two polygons to be congruent, they must have an equal number of sides (and hence an equal number—the same number—of vertices). Two polygons with ''n'' sides are congruent if and only if they each have numerically identical sequences (even if clockwise for one polygon and counterclockwise for the other) side-angle-side-angle-... for ''n'' sides and ''n'' angles.Congruence of polygons can be established graphically as follows:*First, match and label the corresponding vertices of the two figures.*Second, draw a vector from one of the vertices of the one of the figures to the corresponding vertex of the other figure. ''Translate'' the first figure by this vector so that these two vertices match.*Third, ''rotate'' the translated figure about the matched vertex until one pair of corresponding sides matches.*Fourth, ''reflect'' the rotated figure about this matched side until the figures match. If at any time the step cannot be completed, the polygons are not congruent.==Congruence of triangles==SAS and from congruence of triangles, a redirect page. -->: ''See also Solution of triangles.''Two triangles are congruent if their corresponding sides are equal in length, in which case their corresponding angles are equal in size.If triangle ABC is congruent to triangle DEF, the relationship can be written mathematically as::\triangle \mathrm \cong \triangle \mathrmIn many cases it is sufficient to establish the equality of three corresponding parts and use one of the following results to deduce the congruence of the two triangles. In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. So 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 is permitted. In elementary geometry the word ''congruent'' is often used as follows. The word ''equal'' is often used in place of ''congruent'' for these objects. *Two line segments are congruent if they have the same length. *Two angles are congruent if they have the same measure. *Two circles are congruent if they have the same diameter. In this sense, ''two plane figures are congruent'' implies that their corresponding characteristics are "congruent" or "equal" including not just their corresponding sides and angles, but also their corresponding diagonals, perimeters and areas. The related concept of similarity applies if the objects differ in size but not in shape. ==Determining congruence of polygons== For two polygons to be congruent, they must have an equal number of sides (and hence an equal number—the same number—of vertices). Two polygons with ''n'' sides are congruent if and only if they each have numerically identical sequences (even if clockwise for one polygon and counterclockwise for the other) side-angle-side-angle-... for ''n'' sides and ''n'' angles. Congruence of polygons can be established graphically as follows: *First, match and label the corresponding vertices of the two figures. *Second, draw a vector from one of the vertices of the one of the figures to the corresponding vertex of the other figure. ''Translate'' the first figure by this vector so that these two vertices match. *Third, ''rotate'' the translated figure about the matched vertex until one pair of corresponding sides matches. *Fourth, ''reflect'' the rotated figure about this matched side until the figures match. If at any time the step cannot be completed, the polygons are not congruent. ==Congruence of triangles== : ''See also Solution of triangles.'' Two triangles are congruent if their corresponding sides are equal in length, in which case their corresponding angles are equal in size. If triangle ABC is congruent to triangle DEF, the relationship can be written mathematically as: :$\backslash triangle\; \backslash mathrm\; \backslash cong\; \backslash triangle\; \backslash mathrm$ In many cases it is sufficient to establish the equality of three corresponding parts and use one of the following results to deduce the congruence of the two triangles. 抄文引用元・出典: フリー百科事典『 : ''See also Solution of triangles.''Two triangles are congruent if their corresponding sides are equal in length, in which case their corresponding angles are equal in size.If triangle ABC is congruent to triangle DEF, the relationship can be written mathematically as::\triangle \mathrm \cong \triangle \mathrmIn many cases it is sufficient to establish the equality of three corresponding parts and use one of the following results to deduce the congruence of the two triangles.">ウィキペディア（Wikipedia）』 ■: ''See also Solution of triangles.''Two triangles are congruent if their corresponding sides are equal in length, in which case their corresponding angles are equal in size.If triangle ABC is congruent to triangle DEF, the relationship can be written mathematically as::\triangle \mathrm \cong \triangle \mathrmIn many cases it is sufficient to establish the equality of three corresponding parts and use one of the following results to deduce the congruence of the two triangles.">ウィキペディアで「In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. So 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 is permitted.In elementary geometry the word ''congruent'' is often used as follows. The word ''equal'' is often used in place of ''congruent'' for these objects.*Two line segments are congruent if they have the same length. *Two angles are congruent if they have the same measure.*Two circles are congruent if they have the same diameter.In this sense, ''two plane figures are congruent'' implies that their corresponding characteristics are "congruent" or "equal" including not just their corresponding sides and angles, but also their corresponding diagonals, perimeters and areas.The related concept of similarity applies if the objects differ in size but not in shape.==Determining congruence of polygons==For two polygons to be congruent, they must have an equal number of sides (and hence an equal number—the same number—of vertices). Two polygons with ''n'' sides are congruent if and only if they each have numerically identical sequences (even if clockwise for one polygon and counterclockwise for the other) side-angle-side-angle-... for ''n'' sides and ''n'' angles.Congruence of polygons can be established graphically as follows:*First, match and label the corresponding vertices of the two figures.*Second, draw a vector from one of the vertices of the one of the figures to the corresponding vertex of the other figure. ''Translate'' the first figure by this vector so that these two vertices match.*Third, ''rotate'' the translated figure about the matched vertex until one pair of corresponding sides matches.*Fourth, ''reflect'' the rotated figure about this matched side until the figures match. If at any time the step cannot be completed, the polygons are not congruent.==Congruence of triangles==SAS and from congruence of triangles, a redirect page. -->: ''See also Solution of triangles.''Two triangles are congruent if their corresponding sides are equal in length, in which case their corresponding angles are equal in size.If triangle ABC is congruent to triangle DEF, the relationship can be written mathematically as::\triangle \mathrm \cong \triangle \mathrmIn many cases it is sufficient to establish the equality of three corresponding parts and use one of the following results to deduce the congruence of the two triangles.」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.