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Mr. Wolf Tuesday 11/11/08 Geometry Grades 10-12 Unit 6: Similarity Similar Polygons Materials and Resources: Ratio Riddles Warm-up (1 per student) Similar Polygons Notes (1 per student) Similar Polygons Drawing Activity sheet (1 per student) Rulers, protractors (1 pair per student) Exit Ticket (1 per student) PA Standards Addressed: 2.1.8 D. Apply ratio and proportion to mathematical problem situations involving distance, rate, time and similar triangles. Instructional Objectives: Students will be able to define similar and identify figures that are similar. Students will be able to calculate side lengths, angle measures, and scale factors of similar polygons. Time 10 min 1 min 1 min 15 min Activity Warm-up Agenda Homework Check Review Homework min Similar Polygons Notes min Similar Polygons Drawing Activity Description Pass out the Warm-up and review solutions. Review the goals for the day. Spot-check and review solutions Present the HW solutions and answer any questions. Modeling: Pass out the notes sheets and provide students with information. Guiding: Help students complete example problems. Independent Practice: Students will complete the problems on the back of the sheet. Assessment: Review solutions. Modifications: Students with special needs will be given figures to illustrate the problems on the back. Advanced students will be called on when reviewing solutions. Modeling: Pass out the instructions, rulers, and protractors. Guiding: Help students complete the sheet. Independent Practice: Students will draw the four figures and calculate dimensions. Assessment: Sheets will be collected and graded. 1 min 5 min Agenda Conclusion Homework: Pg. 251 #15, 17-21, 24-27 Lesson Reflection: Modifications: Students with special needs will be given one figure and will need only draw the similar figure. Advanced students will be given more challenging dimensions and scale factors. Revisit goals and identify whether they were met. Pass out the Exit Ticket and collect at the bell. Geometry Fall 2008 Name: ________________________ Ratio Riddles Warm-up 1) Find the measures of two complementary angles whose ratio is 4:5. 2) Find the measures of two supplementary angles whose ratio is 11:4. 3) Find the measures of the angles in a triangle whose ratio is 3:4:5. 4) Find the measures of the acute angles of a right triangle whose ratio is 5:7. 5) Find the measures of the angles in an isosceles triangle whose ratio is 3:3:2. 6) Find the measures of the angles in a hexagon whose ratio is 4:5:5:8:9:9. 7) The perimeter of a triangle is 132cm and the lengths of its sides are in the ratio 8:11:14. Find the length of each side. 8) What is the ratio of the measure of an interior angle to the measure of an exterior angle in a regular hexagon? Geometry Fall 2008 Name: ________________________ Ratio Riddles Warm-up 1) Find the measures of two complementary angles whose ratio is 4:5. 2) Find the measures of two supplementary angles whose ratio is 11:4. 3) Find the measures of the angles in a triangle whose ratio is 3:4:5. 4) Find the measures of the acute angles of a right triangle whose ratio is 5:7. 5) Find the measures of the angles in an isosceles triangle whose ratio is 3:3:2. 6) Find the measures of the angles in a hexagon whose ratio is 4:5:5:8:9:9. 7) The perimeter of a triangle is 132cm and the lengths of its sides are in the ratio 8:11:14. Find the length of each side. 8) What is the ratio of the measure of an interior angle to the measure of an exterior angle in a regular hexagon? Geometry Fall 2008 Name: ________________________ Similar Polygons Notes Two polygons are similar if… Example: Polygon PQRST is similar to polygon UVWXY Notation: Because the polygons are similar, the following statements are true: If two polygons are similar, then the ratio of the lengths of two corresponding sides is called the scale factor of the similarity. Example: Given ABC ~ DEF . Calculate the scale factor of the similarity. Use the scale factor to find the values of x and y. Practice Problems: Determine whether the following figures are similar always, sometimes, or never. 1) Two equilateral triangles. _______________ 2) Two isosceles triangles. _______________ 3) Two squares. _______________ 4) Two regular polygons. _______________ 5) An isosceles triangle and a scalene triangle. _______________ 6) Two rhombuses. _______________ 7) A right triangle and a scalene triangle. _______________ 8) Two isosceles triangles. _______________ 9) Two rectangles. _______________ 10) Two regular hexagons. _______________ Given: quadrilateral MATH ~ quadrilateral M’A’T’H’ mY ' _______ mD _______ The scale factor of quadrilateral MATH to quadrilateral M’A’T’H’ is ________. TH _______ M ' A' _______ M ' H ' _______ (in terms of t) The ratio of the perimeters is ___________ Explain why it is not true that quadrilateral THMA ~ quadrilateral A’M’H’T’. Geometry Fall 2008 Name: ________________________ Similar Polygons Drawing Activity Materials: Ruler Protractor Pencil Goal: To construct similar polygons using various scale factors. Figure 1: 1) Draw quadrilateral JKL M with the following dimensions: J 80 K 65 L 137 JK 12cm KL 5cm LM 9cm M 78 MJ 8cm 2) Draw quadrilateral NOPQ so that quadrilateral JKLM ~ quadrilateral NOPQ by a scale factor of 2:3. 3) Calculate the following dimensions of quadrilateral NOPQ . N ________ O ________ P ________ Q ________ NO ________ OP ________ PQ ________ QN ________ Figure 2: 1) Draw ABC with the following dimensions: B 24 A 50 AB 14cm C 106 BC 11cm AC 6cm 2) Draw DEF so that ABC ~ DEF by a scale factor of 2:1. 3) Calculate the following dimensions of DEF . D ________ E ________ F ________ DE ________ EF ________ DF ________ Geometry Fall 2008 Name: ________________________ Exit Ticket Given polygon ABCDE ~ polygon FGHJK by a scale factor of 3:1. Find the following lengths. CD ________ AE ________ Geometry Fall 2008 FG ________ GH ________ Name: ________________________ Exit Ticket Given polygon ABCDE ~ polygon FGHJK by a scale factor of 3:1. Find the following lengths. CD ________ AE ________ FG ________ GH ________