Do Now The ratio of width to length of a swimming pool is 5:8. If the swimming pool is 32 feet long, how wide is it?

Today’s Agenda Unit Reflection on “Ratios, Rates, Proportions, and Percents” Preassessment on “Similar Figures and Scale Factor” on Study Island Lesson / Powerpoint / Notes /Practice Problems

Ratios, Rates, Proportions, Percents - Reflection Write a sentence for each: One thing I learned from this unit was… One thing I still need to work on is… One activity I enjoyed was…

Similar Figures Math 7 Grace Wilday Junior High School “Raise the Praise”

Objective To calculate missing measures of similar figures by using proportions to find the correct measures of at least 8 out of 10 similar figures. NJCCCS A.2 Common Core 7.G.A.1

Congruent Figures Congruent figures – have the same shape and the same size. Example: ΔUVW ≅ ΔXYZ V U W Y X Z

Similar Figures Similar figures – have the same shape but not necessarily the same size. Example: ΔABC ~ ΔDEF A B C D E F

Corresponding Angles and Sides Corresponding angles – angles of similar figures that are in the same relative position Example: angle A and angle D Corresponding sides – sides of similar figures that are in the same relative position Example: side AB and side DE A B C D E F

Practice AB corresponds to _____ BC corresponds to _____ Angle A corresponds to angle _____ A B C X Y Z

Practice KL corresponds to _____ LM corresponds to _____ Angle J corresponds to angle _____ Angle K corresponds to angle _____ R K M L P Q J S

Practice EF corresponds to _____ FG corresponds to _____ Angle H corresponds to angle _____ Angle G corresponds to angle _____ E F G H T U V W

Determining if Figures are Similar Figures are similar if:  The measures of their corresponding angles are equal  The ratios of the lengths of their corresponding sides are proportional

Example AB DE AC DF = = =

Practice Tell whether the figures are similar.

Practice Tell whether the figures are similar.

Practice Tell whether the figures are similar.

Finding Unknown Measures of Similar Figures When figures are similar, you can use a proportion to find missing measures. AB XY BC YZ = 12 x 5 10 =

Practice Use a proportion to find the unknown length.

Practice Use a proportion to find the unknown length.

Practice Use a proportion to find the unknown length.

Real-World Application A six foot tall adult casts a shadow that is 15 feet long. Estimate the height of a child who casts a 10-foot shadow.

Closure A palm tree casts a shadow that is 44 feet long. A 6-foot ladder casts a shadow that is 16 feet long. Estimate the height of the palm tree.