WARM-UP 1.What triangle structures do Similarity and Congruence have in common? 2.Which structures are used only for Congruence? 3.Which structures are used only for Similarity? 4.Why are the ones for congruence not used for Similarity

A TALE OF MANY KITTENS… CAN I HAZ SIMILARITY?

TWO WAYS TO THINK ABOUT SIMILARITY Things you can say once you already know two shapes are similar How to determine whether or not two figures are similar

IF YOU KNOW TWO SHAPES ARE SIMILAR: You can use the similarity statement to: 1.Identify Corresponding Parts 2.Create proportions 3.Determine congruent Correct! Incorrect!

IF YOU KNOW TWO SHAPES ARE SIMILAR: You can use the similarity statement to: 1.Identify Corresponding Parts 2.Create proportions 3.Determine congruent angles Correct! Incorrect!

IF YOU KNOW TWO SHAPES ARE SIMILAR: You can use the similarity statement to: 1.Identify Corresponding Parts 2.Create proportions 3.Determine congruent angles Correct! Incorrect!

IF YOU KNOW TWO SHAPES ARE SIMILAR: You can use the similarity statement to: 1.Identify Corresponding Parts 2.Create proportions 3.Determine congruent angles Next

IF YOU KNOW TWO SHAPES ARE SIMILAR: You can use the similarity statement to: 1.Identify Corresponding Parts 2.Create proportions 3.Determine congruent angles 1 2 3

IN ORDER TO SHOW TWO FIGURES ARE SIMILAR You need to: 1.Identify Corresponding parts 2.Create Proportions 3.Identify Congruent Angles Using one of the following “structures” i.AA ii.SAS iii.SSS

CORRESPONDING… KITTENS?

WHICH PAIR OF CATS ARE CORRESPONDING? WHY?

QUALITY/QUANTITY VS. STRUCTURE “Biggest side” ( Quantity or quality of the side) vs. “The included side of the smallest and medium angles” (Location of the side in the structure of the triangle) Note: Structure makes use of quantity and quality, but just goes a step further.

RATIOS: ONE ITEM OVER ANOTHER We usually try to compare two things that correspond

RATIOS, PROPORTION, SIMILARITY, AND CONGRUENCE If two ratios are equal, we say they are proportional If all of the corresponding sides of a figure are proportional, the figures are similar. If two figures are similar, their corresponding angles are congruent.

ANY QUESTIONS?