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 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 of the other)

Solve for a missing side length: 1) Trapezoid ABCD is similar to trapezoid WXYZ (one is a reflection 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

Solve for a missing side length: 2) Triangle ABC is similar to triangle DEF (one is a rotation 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.

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.

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 (entitled “Practice Work”) 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 of the other) 2)Triangle ABC ~ Triangle DEF: (one is a rotation 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

Solve for a missing side length: 1)Trapezoid ABCD is similar to trapezoid WXYZ (one is a reflection of the other). Solve for the missing side-length. 2)Triangle ABC is similar to triangle DEF (one is a rotation 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

Find the value of “x” in the following similar figures: 1) 2) 3) DATE: ______/_______/_______NAME:_____________________________________________________________________________ E D F 4.5 ft x C A 3 ft 4 ft B A BC D 14 ft 12 ft F G H J x 18 ft LM NO 20 in 12 in QR ST 15 in x

DATE: ______/_______/_______NAME:_______________________________________________________________________________