Geometry. August 19, 2014 Geometry Common Core Test Guide Sample Items. Old or New?????. Old or New?. Old or New?.
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August 19, 2014
Geometry Common Core Test Guide
Grade 8 CCSS-Geometry
Grade 8 Geometry Tasks
High School Geometry Tasks
“The concepts of congruence, similarity, and symmetry can be understood from the perspective of geometric transformation.Fundamental are the rigid motions: translations, rotations, reflections, and combinations of these, all assumed to preserve distance and angles…
Similarity transformations (rigid motions followed by dilations) define similarity in the same way that rigid motions define congruence, thereby formalizing the similarity ideas of "same shape" and "scale factor" developed in the middle grades.”
Common Core State Standards for Mathematics, p74
The reflection R across a given line L, where L is called the line of reflection, assigns each point on L to itself, and to any point P not on L, R assigns the point R(P) which is symmetric to it with respect to L, in the sense that L is the perpendicular bisector of segment joining P to R(P)
Lesson 4: Lined Paper Activity leads to an understanding of similarity.
Similarity in terms of Dilation
Given a dilation with center O and scale factor r, then for any two points P, Q in the plane (when points O, P, Q are not collinear), the lines PQ and P’Q’ are parallel, where P’ = Dilation(P) and Q’ = Dilation(Q), and furthermore, |P’Q’| = r |PQ|.
Lesson 7: Informal Proofs of Properties of Dilations
Two triangles with two pairs of equal corresponding angles are similar.
Use your handout to outline a proof of the theorem.