If two objects are similar then one is an enlargement of the other The rectangles below are similar: Find the scale factor of enlargement that maps A to B Find the scale factor if B was the pre-image. A B 8 cm 16 cm 5 cm 10 cm Scale factor of 2 from A to B Scale factor of ½ from B to A

3.2.1 – Similar triangles – Congruent shapes & flow charts

Remember: 1. Two shapes are similar when their sides are in the same ratio. 2. Corresponding angles in similar shapes are congruent. 4♥4♥4♥4♥ 2.5♥ LN M 8♥8♥8♥8♥ 5♥5♥ XZ Y

If I asked you to prove these triangles were similar, you would have to write 6 (SIX!) similarity statements. MN ~ YZ ML ~ YX LN ~ XZ 4♥4♥4♥4♥ 2.5♥ LN M 8♥8♥8♥8♥ 5♥5♥ XZ Y  M =  Y  N =  Z  L =  X ΔMLN ~ ΔYXZ

If I asked you to prove these triangles were similar, you would have to write 6 more similarity statements. LY ~ XZ LN ~ XM NY ~ MZ 3♥3♥ 12♥ 10♥ L N M 6♥6♥ 20♥ 24♥ X Z Y  M =  N  Y =  Z  L =  X ΔLNY ~ ΔXMZ

What if I asked you to prove these triangles were similar? How many similarity statements would you have to write? LY ~ XZ LN ~ XM NY ~ MZ 3.5♥ 9♥ 8♥8♥ L N M 10.5♥ 24♥ 27♥ X Z Y  M =  N  Y =  Z  L =  X ΔLNY ~ ΔXMZ

Psssst… wanna know a secret? Yes, please.

#1. If you see that 2 pair of corresponding angles have the same measure that means the third one is the same. #2. If you see that ALL of the corresponding sides are in the same ratio, that means all the corresponding angles are congruent. There’s two shortcuts you can use.

70 o 45 o 65 o 45 o These two triangles are similar since their corresponding angles are congruent. 50 o 55 o These two triangles are similar since their corresponding angles are congruent. If 2 triangles have 2 corresponding, congruent angles, then the 3 rd one is also corresponding and congruent THEREFORE the triangles are similar 75 o 50 o = 180 – 125 = 55

This is called AA for ‘angle-angle’

Side Side Side If all three corresponding side lengths share a common ratio, then the triangles are SIMILAR. The other shortcut is called SSS 4♥4♥4♥4♥ 2.5 ♥ LN M 8♥8♥8♥8♥ 5♥5♥ XZ Y These triangles are similar by SSS

Flow charts are used to organize your reasoning Please open your book to page 157 and we’ll go through this together. Pg 157

Quick Check 1.What is one shortcut to prove triangles similar? 2.What is another shortcut to prove triangles similar? 3.If the scale factor between 2 triangles is 3, and one of the sides measures 4 units, what is the length of the corresponding side? 4.ΔABC ~ ΔLMN Give me one similarity statement between these triangles 5.Give me another. 6.Give me another. 7.What is the sum of degrees in a triangle? 8.What is the sum of degrees in a quadrilateral? 9.What is the sum of degrees in a right isosceles triangle? 10.What is the sum of degrees in a right isosceles trapezoid? 11.What is the exact answer to: 5√3 + 2√3 12.What is the exact answer to: √9 + √25

Your assignment Pg ; 48-52, 59-63