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## M & M Ratio Activity/ Chapter 8/ Flashlight Activity

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**M & M Ratio Activity/ Chapter 8/Flashlight Activity**MA.912.G.2.2 MA.912.G.3.4**8.1 Ratio and Proportion**MA.912.G.2.2 MA.912.G.3.4**8.1 Ratio and Proportion**• Ratio of a to b – if a and b are two quantities that are measured in the same units then the ratio of a to b can be written as and as a:b. • Ratios are usually written in simplified form. The ratio 6:8 would be written 3:4.**8.1 Ratio and Proportion**• The perimeter of a rectangle ABCD is 60 centimeters. The ratio of AB : BC is 3:2. Find the length and width of the rectangle.**8.1 Ratio and Proportion**• The perimeter of a rectangle ABCD is 60 centimeters. The ratio of AB : BC is 3:2. Find the length and width of the rectangle. • Solution: Because the ratio of AB : BC is 3:2, you can represent the length AB as 3x and the width BC as 2x. • 2l + 2w = P (formula for perimeter) • 2(3x) + 2(2x) = 60 • 6x +4x = 60 • 10x = 60 • X = 6 • So, ABCD has a length of 18 centimeters and a width of 12 centimeters.**8.1 Ratio and Proportion**• Proportion – an equation that has two ratios. IF the ratio of is equal to the ratio , then the following proportion can be written: • = • The numbers a and d are extremes of the proportion. The numbers b and c are the means of the proportion.**8.1 Ratio and Proportion**• Properties of Proportions • 1. Cross Product Property – The product of the extremes equals the product of the means. IF =, then ad = bc • 2. Reciprocal Property – IF two ratios are equal, then their reciprocals are also equal. IF =, then =**8.1 Ratio and Proportion**• = • =**8.1 Ratio and Proportion**• Homework: Page 461 10-16, 26-28, 34-46 even**Steps to the activity**• Open your package of M & Ms • Sort all your colored M & Ms • Count each color separately and record the amount on your piece of paper • Count the TOTAL number of M & Ms and record that amount**Let’s Begin**• Write the answer to all the ratios as a fraction, using a colon, and the word to. • Example: What is the ratio of blue M & Ms to red M & Ms (In my bag: blue= 4 And red= 8) • 4/8 = ½ , 1:2 or 4:8, 1 to 2 or 4 to 8**Now answer the following:**• What is the ratio of greenM & Ms to yellow M & Ms • What is the ratio of blue M & Ms to Red M & Ms • What is the ratio of brownM & Ms to the total number of M & Ms**Ready for some more?**• What is the ratio of greenand redM & Ms to the total of M & Ms • Record the ratio of blueM & Ms to the total number of yellowand orangeM & Ms • Record your favorite color of M & Ms to the total number of M & Ms (You must write down your favorite color)**Need just a little more practice.**• Record the ratio of orangeM & Ms to greenand yellowM & Ms • What is the ratio of your least favorite M & Ms to the total M & Ms • My favorite color is green. What is the ratio of my favorite color & your favorite color of M & Ms to the total number of M & Ms**Are you getting hungry?**• Create a table showing your color of M & Ms and the amounts**You are almost finished!**• Please put your name on your paper • Now you may eat your M & Ms!!!!! • I hope you had fun with ratios**8.3 Similar Polygons**MA.912.G.3.4**8.3 Similar Polygons**• Similar Polygons – the correspondence between two polygons such that their corresponding angles are congruent and the lengths of corresponding sides are proportional. • Scale Factor – the ratio of the lengths of two corresponding sides of similar polygons.**8.3 Similar Polygons**• Theorem 8.1 If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths. If KLMN ~ PQRS, then = = = =**8.3 Similar Polygons**• Homework: Page 476 8-42 even**8.4 Similar Triangles**MA.912.G.3.4**8.4 Similar Triangles**• Postulate 22 Angle – Angle Similarity Postulate If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. If JKL = XYZ and KJL = YXZ, then JKL ~ XYZ**8.4 Similar Triangles**• Homework: Page 484 18-26, 34-46 even**8.5 Proving Triangles are Similar**MA.912.G.3.4**8.5 Proving Triangles are Similar**• Theorem 8.2 Side-Side-Side (SSS) Similarity Theorem If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar. If = = Then ABC ~ PQR**8.5 Proving Triangles are Similar**• Theorem 8.3 Side-Angle-Side (SAS) Similarity Theorem IF an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar If X = M and = Then XYZ ~ MNP**8.5 Proving Triangles are Similar**• Homework: Page 492 6-26 even**8.6 Proportions and Similar Triangles**MA.912.G.3.4**8.6 Proportions and Similar Triangles**• Theorem 8.4 Triangle Proportionality Theorem If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally. If TU ǁ QS, then =**8.6 Proportions and Similar Triangles**• Theorem 8.5 Converse of the Triangle Proportionality Theorem IF a line divides two sides of a triangle proportionally, then it is parallel to the third side. If = , then TU ǁ QS.**8.6 Proportions and Similar Triangles**• Theorem 8.6 IF three parallel lines intersect two transversals, then they divide the transversals proportionally. If r ǁ s and s ǁ t, and l and m Intersect r, s, and t, then = .**8.6 Proportions and Similar Triangles**• Theorem 8.7 IF a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides. If CD bisects LABC, then =**8.6 Proportions and Similar Triangles**• Homework: Page 502 12-30 even**End of Chapter Review**• Homework: Page 519 1-18