M & M Ratio Activity/ Chapter 8/Flashlight Activity

MA.912.G.2.2MA.912.G.3.4

8.1 Ratio and ProportionMA.912.G.2.2MA.912.G.3.4

8.1 Ratio and ProportionRatio 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 ProportionThe 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 ProportionThe 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) = 606x +4x = 6010x = 60X = 6So, ABCD has a length of 18 centimeters and a width of

12 centimeters.

8.1 Ratio and ProportionProportion – 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 ProportionProperties of Proportions1. Cross Product Property – The product of

the extremes equals the product of the means.

IF =, then ad = bc2. Reciprocal Property – IF two ratios are

equal, then their reciprocals are also equal.

IF =, then =

8.1 Ratio and Proportion =

=

8.1 Ratio and ProportionHomework: Page 461 10-16, 26-28, 34-46

even

Steps to the activity

Open your package of M & MsSort all your colored M & MsCount each color separately and record the

amount on your piece of paperCount 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 green M & Ms to yellow

M & MsWhat is the ratio of blue M & Ms to Red M &

MsWhat is the ratio of brown M & Ms to the

total number of M & Ms

Ready for some more?What is the ratio of green and red M & Ms

to the total of M & MsRecord the ratio of blue M & Ms to the total

number of yellow and orange M & MsRecord 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 orange M & Ms to green

and yellow M & MsWhat 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 paperNow you may eat your M & Ms!!!!!I hope you had fun with ratios

8.3 Similar PolygonsMA.912.G.3.4

8.3 Similar PolygonsSimilar 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 PolygonsTheorem 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 PolygonsHomework: Page 476 8-42 even

8.4 Similar TrianglesMA.912.G.3.4

8.4 Similar TrianglesPostulate 22 Angle – Angle Similarity

PostulateIf 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 SimilarMA.912.G.3.4

8.5 Proving Triangles are SimilarTheorem 8.2 Side-Side-Side (SSS) Similarity

TheoremIf 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 SimilarTheorem 8.3 Side-Angle-Side (SAS) Similarity

TheoremIF 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 SimilarHomework: Page 492 6-26 even

8.6 Proportions and Similar TrianglesMA.912.G.3.4

8.6 Proportions and Similar TrianglesTheorem 8.4 Triangle Proportionality

TheoremIf 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 TrianglesTheorem 8.5 Converse of the Triangle

Proportionality TheoremIF 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 TrianglesTheorem 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 mIntersect r, s, and t, then = .

8.6 Proportions and Similar TrianglesTheorem 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 TrianglesHomework: Page 502 12-30 even

End of Chapter ReviewHomework: Page 519 1-18