It might seem easy to equate two figures being congruent to having same size and same shape. So how do these facts about rigid motions and symmetry relate to congruence? We define two figures in the plane asĬongruent if there exists a finite composition of basic rigid motions that maps one figure onto the other. We noted that a symmetry is a rigid motion that carries a figure to itself.Defining congruenceīy means of rigid motions extends this notion of sameness to arbitrary figures, while clarifying the meaning in an Measure is well characterized by the existence of a rigid motion mapping one thing to another.
Respect if they have the same length (respectively, degree measure), and thus, sameness of these objects relating to We think of two segments (respectively, angles) as the same in an important We observed that rotations, translations, and reflections-and thus all rigid motions-preserve the lengths of.Let us recall some facts related to congruence that appeared previously in this unit. Precision and focus on the language with which we discuss it. (8.G.A.2)Īs with so many other concepts in high school Geometry, congruence is familiar, but we now study it with greater (1) Understand that a two-dimensional figure is congruent to another if the second can be obtained from theįirst by a sequence of rotations, reflections, and translations and (2) describe a sequence that exhibits theĬongruence between two congruent figures. In Grade 8, we introducedĪnd experimented with concepts around congruence through physical models, transparencies, or geometry software. We have been using the idea of congruence already (but in a casual and unsystematic way). This involves being able to repeat the definition of congruence and use it in an accurate and effective way.Ĭonstruct and Apply a Sequence of Rigid Motions Students begin developing the capacity to speak and write articulately using the concept of congruence.Worksheets for Geometry, Module 1, Lesson 19 New York State Common Core Math Geometry, Module 1, Lesson 19
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