In question a, they should notice a reflection and by observation, they can tell that the two figures are congruent. In question 2, students look at polygons in the coordinate grid. Students apply visual reasoning to determine that Ruby's configuration could be turned 180˚ and line up exactly with Kha Di's. While all the figures have 6 unit squares (equal areas) only Ruby's and Kha Di's sketches are congruent. Instead of starting with polygons, students look at a set of 4 figures composed of unit squares and determine which two are congruent. Informally, one figure should land directly on top of the other. If two figures are congruent, then there must be a sequence of transformations to move one onto the other. Today we want students to realize that not only do rigid transformations keep figures congruent, but the reverse is true as well. They also have observed that rigid motions keep sides and angles congruent and that the image is the "same" as the preimage (in terms of shape and size). Coming into this lesson, students have a partial understanding of congruence, mainly referring to angles with equal measures or segments with equal lengths. Today's lesson is the essential link between everything students have learned about rigid transformations and the big idea of congruence. Day 19: Random Sample and Random Assignment.Day 18: Observational Studies and Experiments.Day 13: Probability using Tree Diagrams.Day 12: Probability using Two-Way Tables.Day 6: Scatterplots and Line of Best Fit.Day 3: Measures of Spread for Quantitative Data.Day 2: Measures of Center for Quantitative Data.Day 4: Surface Area of Pyramids and Cones.Day 2: Surface Area and Volume of Prisms and Cylinders.Day 1: Introducing Volume with Prisms and Cylinders.Day 9: Area and Circumference of a Circle.Day 6: Inscribed Angles and Quadrilaterals.Day 5: Perpendicular Bisectors of Chords.Day 1: Coordinate Connection: Equation of a Circle.Day 4: Using Trig Ratios to Solve for Missing Sides.Unit 7: Special Right Triangles & Trigonometry.Day 7: Area and Perimeter of Similar Figures.Day 6: Proportional Segments between Parallel Lines.Day 2: Coordinate Connection: Dilations on the Plane.Day 1: Dilations, Scale Factor, and Similarity.Day 9: Regular Polygons and their Areas.Day 8: Polygon Interior and Exterior Angle Sums.Day 4: Coordinate Connection: Quadrilaterals on the Plane.
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