THE CRITICAL ATTRIBUTES OF SIMILARITY, INCLUDING RATIOS WITHIN AND BETWEEN SIMILAR SHAPES Including, but not limited to: Congruent of equal measure, having exactly the same size and same shape – Similar shapes shapes whose angles are congruent and side lengths are proportional (equal scale factor) – Notation for similar shapes Symbol for similarity (~) read as “similar to” Ex: ABCD ~ is read as is similar to A prime B prime C prime and A’B’C’D’ “ABCD D prime” The order of the letters determines corresponding side lengths and angles Attributes of similar shapes Corresponding sides are proportional. Corresponding angles are congruent. Ex: Generalizations of similarity A scale factor A scale factor >1 increases the linear dimensions of the shape. Ratios comparing lengths within each shape or between shapes will determine if the shapes are similar. Shapes that are same shape, but a different are not always similar shapes. “the size” Corresponding sides are proportional, while corresponding angles are congruent. There is a multiplicative relationship between the lengths of corresponding sides. Note(s): Grade Level(s): Grade 7 introduces generalizing the critical attributes of similarity, including ratios within and between similar shapes. Various mathematical process standards will be applied to this student expectation as appropriate. TxRCFP: Representing and applying proportional relationships TxCCRS: III.C. Geometric Reasoning Connections between geometry and other mathematical content strands – IV. Measurement Reasoning VIII. Problem Solving and Reasoning IX. Communication and Representation X. Connections
THE CRITICAL ATTRIBUTES OF SIMILARITY, INCLUDING RATIOS WITHIN AND BETWEEN SIMILAR SHAPES Including, but not limited to: Congruent – of equal measure, having exactly the same size and same shape Similar shapes – shapes whose angles are congruent and side lengths are proportional (equal scale factor) Notation for similar shapes Symbol for similarity (~) read as “similar to” Ex: ABCD ~ A’B’C’D’ is read as “ABCD is similar to A prime B prime C prime and D prime” The order of the letters determines corresponding side lengths and angles Attributes of similar shapes Corresponding sides are proportional. Corresponding angles are congruent. Ex: Generalizations of similarity A scale factor A scale factor >1 increases the linear dimensions of the shape. Ratios comparing lengths within each shape or between shapes will determine if the shapes are similar. Shapes that are “the same shape, but a different size” are not always similar shapes. Corresponding sides are proportional, while corresponding angles are congruent. There is a multiplicative relationship between the lengths of corresponding sides. Note(s): Grade Level(s): Grade 7 introduces generalizing the critical attributes of similarity, including ratios within and between similar shapes. Various mathematical process standards will be applied to this student expectation as appropriate. TxRCFP: Representing and applying proportional relationships TxCCRS: III.C. Geometric Reasoning – Connections between geometry and other mathematical content strands IV. Measurement Reasoning VIII. Problem Solving and Reasoning IX. Communication and Representation X. Connections