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Math 2: Algebra 2, Geometry and Statistics Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434 Name: Date: Similarity β Notes and Problems Isometry: a transformation is an isometry if it preserves distance. Transformations that are isometries include: ______________________, _______________________, and _______________________. Uniform Scaling: is a linear transformation that __________________________ (increases) or __________________(diminishes) objects by a scale factor that is the same in all directions. Uniform Scaling of a figure creates ______________________________ figures. Similar Figures: geometric figures that have congruent corresponding _______________________ and proportional corresponding _________________________________. Scale Factor/Similarity Ratio: the _________________ between the side lengths of two __________________ polygons. Ex 1: In the figure below βπ΄π΅πΆ~βπ·πΈπΉ. List the 3 pairs of congruent corresponding angles and the three pairs of proportional corresponding sides. Find the scale factor for the two triangles. Congruent Corresponding Angles Proportional Corresponding Sides Scale Factor/Similarity Ratio Math 2: Algebra 2, Geometry and Statistics Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434 Name: Date: Ex 2: A triangle has coordinates A (β9, β1), B (β7, 6), and C (β4, 2). A second triangle has coordinates Aβ (10, β4), Bβ (6, 10) and Cβ (0, 2). Graph the triangles and use coordinate geometry to show that the corresponding sides of each triangle are proportional. 10 8 6 4 2 β 10 β5 5 β2 β4 β6 β8 10 Math 2: Algebra 2, Geometry and Statistics Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434 Name: Date: Homework 66: Similar Polygons Directions: Are the polygons similar? If they are, write a similarity statement, and give the similarity ratio. If they are not, explain why not. 1. 2. 3. 4. 5. 6. Math 2: Algebra 2, Geometry and Statistics Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434 Name: Date: Directions: LMNO ~ HIJK. Complete the congruence statements and proportions. 7. 10. β π β β ____ !" !" = !" 8. β πΎ β β _____ 11. !" = !" !" 9. β π β β _______ 12. Directions: Use the similarity statements to find the value of x. 13. βπ΄π΅πΆ~βπΈπΉπΊ x= 14. SPQR ~ OLMN x= 15. WXYZ ~ EFGH x= 16. JKLM ~ PQRS x= !" !" = !" Math 2: Algebra 2, Geometry and Statistics Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434 Name: Date: 17. Quadrilateral DFEG has coordinates D (2, β2), F (β4, 6), E (β8, 3), and G (β2, β5). A transformed figure has coordinates Dβ (2, β2), Fβ 423, 0 , Eβ 323, 1 1 3 , and Gβ 1, β 2 3 . Determine whether these figures are similar or not. Donβt forget to attend to angles. Prove your conclusion using coordinate geometry. 10 8 6 4 2 β 10 β5 5 β2 β4 β6 β8 10 Math 2: Algebra 2, Geometry and Statistics Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434 Name: Date: 18. Triangle KJI has coordinates J (6, β2), K (12, 4) and (I (2, 2), and mβ πΎ = 34°. It is transformed such that the new coordinates are Jβ (β4, 0), Kβ (β7, β3) and Iβ (β2, β2) and πβ πΌ ! = 56°. Determine whether these figures are similar or not. Donβt forget to attend to angles. Prove your conclusion using coordinate geometry. 10 8 6 4 2 β 10 β5 5 β2 β4 β6 β8 10