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Are the polygons congruent? Section 7.1.1 Objective G-CO.A G-CO.B Pumas will determine missing side lengths of similar polygons identify congruent polygons using the Pythagorean Theorem identify congruent polygons using the Triangle Angle Sum Theorem determine if two triangles are congruent by comparing all three corresponding angle measurements and all three corresponding side lengths Similar Polygons Methods and Meanings In your notebook, copy the following: Two polygons are similar if a sequence of rigid transformations, followed possibly by a dilation (enlargement or reduction), maps one polygon onto the other. Two similar polygons have parts that correspond (match up) with each other. For example, if ∆ABC is similar to ∆DEF, then vertex A corresponds to vertex D, C to F, and B to E. Also, AB corresponds to DE, AC corresponds to DF, and BC corresponds to EF. Similar Polygons Methods and Meanings In your notebook, copy the following: Corresponding angles of two similar polygons have the same measures, but corresponding side lengths might be different. The scale factor is the ratio that indicates how the side lengths of two similar polygons are related. The scale factor can be found by writing a ratio between the lengths of any pair of corresponding sides as Similar Polygons Methods and Meanings In your notebook, copy the following: For example, the two similar triangles above are related by a scale factor of because the side lengths of the new triangle can be found by multiplying any side length of the original triangle by . A scale factor greater than 1 enlarges a shape (makes it larger). A scale factor between zero and 1 reduces a shape (makes it smaller). If a scale factor between two shapes is equal to 1, then the two similar shapes are also congruent. Congruent Polygons Problem 7-3 Figures are drawn to scale Congruent Polygons Problem 7-3 In your notebook, answer the following: Which of the polygons on the previous slide appear to be congruent? What sequence of rigid transformations demonstrates the congruence between the polygons? For each pair of congruent polygons, what can you say about the corresponding angle measures and side lengths? Considering the definition of congruent polygons, why would this have to be true? Congruent Polygons Problem 7-4 In your notebook, complete the following: Sketch the triangles above on your paper. Are the triangles congruent? If so, what is the sequence of rigid transformations that maps the triangle on the left onto the triangle on the right? If the triangles are not congruent, explain why not. Congruent Polygons Problem 7-5 Read the following and identify any questions you have about them. To represent the fact that two polygons are congruent, use the symbol “ ”. For example, if there is a sequence of rigid transformations that maps ΔABC onto ΔDEF, then you know they are congruent and this can be stated as ΔABC ΔDEF. The order of the letters in the name of each triangle identifies which sides and angles correspond. For example, the congruence statement ΔABC ΔDEF, indicates that A corresponds to D and that BC corresponds to EF. Congruent Polygons Problem 7-5 In your notebook, complete the following: Luis wanted to write a statement to convey that the two triangles above are congruent. He started with “ΔMNP …”, but got stuck because the triangles were not oriented the same way. Complete Luis’s statement for him and explain how you determined your answer. Congruent Polygons Problem 7-5 In your notebook, complete the following: What sequence of rigid transformations would map the triangle on the left onto the one on the right? Label the triangles and then write a congruence statement for the triangles below which you sketched in your notebook. Be prepared to justify your thinking.