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students build on their experiences with perpendicular bisectors to answer questions about allocating resources in a real-world situation.
G2 Congruence
Before starting this unit, students are familiar with rigid transformations and congruence from work in grade 8. They have experimentally conRrmed properties of rigid transformations, and informally justiRed that Rgures are congruent by Rnding a sequence of rigid transformations that takes one Rgure onto the other. Students have primarily explored rigid transformations on grids, where they have additional structure to help them Rgure out speciRc rigid transformations that will take one Rgure onto the other.
In this unit, rigid transformations are primarily used to justify the triangle congruence theorems of Euclidean geometry: Side-Side-Side Triangle Congruence, Side-Angle-Side Triangle Congruence, and Angle-Side-Angle Triangle Congruence.
Students justify that for each set of criteria, a sequence of rigid motions exist that will take one triangle onto the other. In middle school, they focused on speciRc examples and Rnding speciRc sequences of rigid motions (for example, students might justify that two triangles on the coordinate plane are congruent because they can Rnd a reSection across the x-axis and a horizontal translation of two units that takes one triangle onto the other). In this unit, students learn to explain how, in general, two triangles with all three pairs of corresponding side lengths congruent can be mapped onto one another using a more general sequence of rigid motions (for example, students might justify that they can translate by a directed line segment from the vertex of one triangle to the corresponding vertex of another, rotate around that vertex until a pair of corresponding sides of the triangles coincide, and reSect across that side so that all three corresponding vertices coincide).
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