#### Transcript Musical Math

Materials Reminders Get out your agenda if you see your name below. I would like to have you in my FLEX Wednesday. Period 2 Period 7 Use the Pythagorean Theorem to determine whether or not the following triangle is a right triangle. 3 1 2 4-7 Similar Polygons How do I identify similar polygons and find the missing measures of similar polygons? Important Vocabulary Polygon – three or more attached line segments in a plane that for a closed figure Similar Polygons (symbol A~B) – polygons with the same exact shape but possibly differing in size (think enlargements or reductions) Corresponding Parts (A ↔ B) – parts of two or more similar figures that match Important Vocabulary Congruent – parts of two figures that have the same measure Scale Factor – what you would multiply the corresponding sides of one similar figure by to get a second similar figure Questions: How do I identify similar polygons? Notes: Steps 1. Find the ratios between all of the corresponding sides of the two figures 2. Determine (using division) whether or not all of the ratios are equal 3. If the ratios are equal, the polygons are similar Example: 2 5 3 7.5 2 = 0. 6 3 5 = 0. 6 7.5 Beause the ratios of the corresponding sides are equal, the figures are similar. Concept Check 1. Get into groups of 2 and get one WHITE BOARD and a DE marker 2. Determine whether the following two figures are similar. 10 5 4 8 7 15 3. Be prepared to share with the class. Questions: How do I determine the scale factor between two similar figures? Notes: Steps 1. Divide a measure on the NEW figure by the corresponding measure on the OLD figure. 2. The result is the SCALE FACTOR. Example: 1 A 3 B The scale factor from triangle A (OLD) to triangle B (NEW) is: 𝑁𝐸𝑊 3 = =3 𝑂𝐿𝐷 1 Concept Check 1. Get into groups of 2 and get one WHITE BOARD and a DE marker 2. Find the listed scale factors for the following similar figures. 1. From trapezoid A to trapezoid B 2. From trapezoid B to trapezoid A 4 A 12 B 3. Be prepared to share with the class. Questions: How do I use proportions to find missing measures? Notes: Steps 1. Set up a proportion using two corresponding sides with known measures and two corresponding sides with one unknown measure (the missing measure) 2. Find the cross products 3. Solve for the variable Example: 5 2 A 3 2 3 = 5 𝑥 B 2𝑥 = 15 𝑥 = 7.5 x This is also the scale factor from A to B Concept Check 1. Get into groups of 2 and get one WHITE BOARD and a DE marker 2. Use the concept of PROPORTIONS to find the missing measure, x, on the following similar figures. 0.7 2.1 x 2.2 3. Be prepared to share with the class. Homework Page 222-223; 1-12 and 18-19 AND Cornell Notes Summary