Name:________________________________________________________________________________Date:_____/_____/__________ 1) Jack spent 20% of his savings at the store. If he spent $45, how much did he have in his savings to begin with? 2) Sarah has 30 beanie boo stuffed animals. She decides to give 40% to charity. How many does she give away ? 3) 12 out of 21 total kids in the class have a TV in their room. What percent is this? 4) Mike P. and a lady friend are out to dinner. The bill is $42. If Mike wants to leave an 18% tip, how much will his tip be? 5) Gabby and Olivia are shopping. Gabby sees some sunglasses that are originally $35, but are on sale for 40% off. What is the sale price? 6) Alex is at Party City for some fiesta supplies. His subtotal is $ If the sales tax is 6%, what is his total? Use the percent proportion formula in order to solve the following consumer application (tax, tip, discount) problems:

Today’s Lesson: What: similar Figures Why: To use proportions to solve problems involving similar figures. What: similar Figures Why: To use proportions to solve problems involving similar figures.

Vocabulary: Similar figure– figures that are the same shape, but a different ____________________. Corresponding sides are ________________. Corresponding angles are _______________. ~ symbol – means “is __________________ to.” size proportional congruent SAME shape! DIFFERENT size! CONGRUENT angles! PROPORTIONAL sides! similar

Identifying corresponding sides: A B D C X Y Z W 1. Side AD corresponds to side _____. 2. Side AB corresponds to side _____. 3. Side BC corresponds to side _____. 4. Side CD corresponds to side _____. 5. Angle X corresponds to angle _____. 6. Angle Z corresponds to angle _____. WZ WX XY YZ B D 1) Trapezoid ABCD ~ Trapezoid WXYZ : (one is a reflection/dilation of the other)

Identifying corresponding sides: 1. Side AB corresponds to side _____. 2. Side AC corresponds to side _____. 3. Side BC corresponds to side _____. 4. Angle A corresponds to angle _____. 5. Angle B corresponds to angle _____. DE B A C E D F DF EF D E 2) Triangle ABC ~ Triangle DEF: (one is a rotation/dilation of the other) If Angle B measures 35 degrees, then what is the measure of angle E? _____ 35° Corresponding angles are CONGRUENT!

Solve for a missing side length: 1) Trapezoid ABCD is similar to trapezoid WXYZ (one is a reflection/dilation of the other). Solve for the missing side-length. AB D C X Y Z W 5 cm 2 cm 12.5 cm ? x = 5 cm Write corresponding sides as a ratio on each side of the proportion... 5x = Notice that this is BIG on top and SMALL on bottom!

Solve for a missing side length: 2) Triangle ABC is similar to triangle DEF (one is a rotation/dilation of the other). Solve for the missing side-length. B A C E D F 9 cm ? 7.2 cm 4 cm x = 5 cm

Solve for a missing side length: 3) 2 Similar Triangles – What is the value of “x”? 12 in. 10 in. 16 in. x x = 19.2 in.

Solve for a missing side length: 4)Scenario: The length and width of a rectangular box are 24 in. and 14 in. respectively. Another rectangular box has a length of 12 in. What is the smaller box’s width? x = 7 in.

Video to accompany tree/shadow problem in your notes (Problem #5):

Solve for a missing side length: 5) A 9.5 ft. tall tree casts a shadow 15 ft. in length. A nearby building casts a shadow that is 45 ft. in length. How tall is the building? x 9.5 ft 15 ft 45 ft x = 28.5 ft.

Similar figure SPEED “DATING”! Time for... Teacher will give directions...

END OF LESSON The next slides are student copies of the notes for this lesson. These notes were handed out in class and filled-in as the lesson progressed. NOTE: The last slide(s) in any lesson slideshow represent the homework assigned for that day.

Identifying corresponding sides: Math-7 NOTES DATE: ______/_______/_______ What: similar Figures Why: To use proportions to solve problems involving similar figures. What: similar Figures Why: To use proportions to solve problems involving similar figures. NAME: Vocabulary: Similar figure – figures that are the same shape, but a different _________. Corresponding sides are __________________________. Corresponding angles are _________________________. ~ symbol – means “is ___________________ to.” AB D C X Y Z W 1)Trapezoid ABCD ~ Trapezoid WXYZ : (one is a reflection/dilation of the other) 2)Triangle ABC ~ Triangle DEF: (one is a rotation/dilation of the other) 1.Side AD corresponds to side _____. 2.Side AB corresponds to side _____. 3.Side BC corresponds to side _____. 4.Side CD corresponds to side _____. 5.Angle X corresponds to angle _____. 6.Angle Z corresponds to angle _____. 1.Side AB corresponds to side _____. 2.Side AC corresponds to side _____. 3.Side BC corresponds to side _____. 4.Angle A corresponds to angle _____. 5.Angle B corresponds to angle _____. SAME shape! DIFFERENT size! CONGRUENT angles! PROPORTIONAL sides! B A C E D F If Angle B measures 35 degrees, then What is the measure of Angle E? _____

Solve for a missing side length: 1)Trapezoid ABCD is similar to trapezoid WXYZ (one is a reflection/dilation of the other). Solve for the missing side-length. 2)Triangle ABC is similar to triangle DEF (one is a rotation/dilation of the other). Solve for the missing side-length. 3)2 Similar Triangles – What is the value of “x”? 4)Scenario: The length and width of a rectangular box are 24 in. and 14 in. respectively. Another rectangular box has a length of 12 in. What is the smaller box’s width? 5)A 9.5 ft. tall tree casts a shadow 15 ft. in length. A nearby building casts a shadow that is 45 ft. in length. How tall is the building? AB D C X Y Z W 5 cm 2 cm 12.5 cm ? x 9.5 ft 15 ft 45 ft 12 in. 10 in. 16 in. x B A C E D F 9 cm ? 7.2 cm 4 cm

DATE: ______/_______/_______NAME:_______________________________________________________________________________