Warm Up

1A ratio is a comparison of two numbers such as a : b. ABC6810Now try to reduce the fraction. Ratio:When writing a ratio, always express it in simplest form.Example:Ratio

1Type notes here

2Proportion: An equation that states that two ratios are equal.TermsProportion

First TermSecond TermThird TermFourth TermTo solve a proportion, cross multiply the proportion2Type notes here

Practice

Practice worksheetOn my websitewww.mshalllovesmath.wordpress.comPeriod 2Proportions

StandardG-SRT 2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.ObjectiveUsing prior knowledge of proportions and angles and given knowledge about similar triangles students will determine if triangles are similar.Similar FiguresDefinition: Two figures are similar if their corresponding sides are proportional, and their corresponding angles are equal. Similar figures have the same shape but possibly different sizes.

SimilarityStatement:ABC ~ DEF

Notes: ~ => is similar toThe order of the letters matters!

AFEDCBMatch pairs of similar shapes.81) Corresponding angles are congruent:

2) Corresponding sides are proportional:

AFEDCB

= = The fractions all reduce to a common similarity ratio.Example 1Identify the pairs of congruent angles and corresponding sides.N Q and P R, M T

0.5

Example 2Identify the pairs of congruent angles and corresponding sides.

B G and C H, A J.

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50Ex 3. Identify the pairs of congruent angles and corresponding sides.142Are the triangles similar? How do you know?12

Congruent AnglesIdentify the pairs of congruent angles and corresponding sides.N M, L P, S J

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50Identify the pairs of congruent angles and corresponding sides.14PolygonDetermine whether the polygons are similar. If so, write the similarity ratio and a similarity statement.

A E, B F, C G, and D H.

Ratios and Proportion worksheets and similar figures and proportions

Picture frame problem Objective: Students will use their prior knowledge on proportions, and similarity to solve for a missing side. Example 1 SUT ~ SRQ. Use a proportion to solve for x.SQRTUS21718x

Example 2:Set up a proportion and find x.

RDE ~ AMLRx8DE12MLA9

Example 3SUT ~ SRQ. Use a proportion to solve for x.5x3x3

Example 4 PST~ PQRSolve for x.

6124x

More practice with proportions and similar figuresGo to www.mshalllovesmath.wordpress.com

Click on your period and open the linkMore practice with proportions and similar figures

Work on it on paper or on adobe readerG.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Objective: Students will investigate AA criterion and SSS criterion for triangle similarity and be able to use the criterion to identify similar triangles Side-Side-Side (SSS~)aefdcbIf ___ = ___ = ___, then the triangles are similar. Note: If sides are proportional, then corresponding angles must be congruent, and the s ~.PQNMLR

Example 1:Are the two triangles similar?Why or why not?Yes SSS~

What is the similarity statement?_ZHT______ ~ _WKR_______

If mT = 39 and mW = 57, find the measures of the remaining angles in both triangles. 3864912HZTKWRAre they giving us side lengths or angle measures?Missing Angle Measure- 84 25Example 2:Are the two triangles similar?Why or why not?Yes SSS~

What is the similarity statement?__ZHT_____ ~ _WRT_______

If mT = 41 and mR = 67, find the measures of the remaining angles in both triangles. 516818910HZTKWRAre they giving us side lengths or angle measures?Missing Angle Measure- 84 26Angle-Angle (AA ~)If _____ pairs of ________________ angles are ______________, then the triangles are similar. Note: If ____ ____ and ____ ____, then the corresponding sides must be proportional and the s ~..aefdcbPQNMLR2correspondingcongruentExample Are the two triangles similar?Why or why not?Yes AA~

What is the similarity statement?_______ ~ ________

61 B5312FCEQS5361Are they giving us side lengths or angle measures?Are they giving us side lengths or angle measures?6628Focus QuestionWhy do we only need to show that TWO pairs of corresponding angles are congruent to prove similarity?

Think: How did you findthe missing angle in BOTHtriangles?

61 B53FCEQS5361Example:Are the two triangles similar?Why or why not?

No the triangles do not Have 2 corresponding congruent angles 583532 and 55NO not similar30Classwork #3See Worksheet CW #3 SSS~ and AA~