1. 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) Andrew and a lady friend are out to dinner. The bill is $42. If Andrew 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 $44.99. If the sales tax is 6%, what is his total? Tax, Tip, Discounts: Watch out for 2- step problems...

2. 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.

3. 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

4. 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)

5. 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!

6. 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 = 25 5 5 Notice that this is BIG on top and SMALL on bottom!

7. 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

8. 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.

9. 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.

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

11. 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.

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

13. IXL: X.13 homework

14. END OF LESSON The next slides are student copies of the notes and handouts for this lesson. These were handed out in class and filled-in as the lesson progressed.

15. 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? _____

16. 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

17. DATE: ______/_______/_______ NAME:___________________________________________________________________________ For the problems that require a proportion (solving for missing side-length), use below scratch space. HOWEVER, some problems are asking for a missing angle. These do NOT require a proportion, and therefore do NOT require scratch: Example: This type uses a proportion. This type does NOT require a proportion, so you do not have to show work! Answer : 113° because corresponding angles are CONGRUENT!!

19. DATE: ______/_______/_______NAME:_______________________________________________________________________________