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 TA L E O F M A N Y K I TT E N S …

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 Parts2. Create proportions3. Determine congruent

Correct!

Incorrect!

IF YOU KNOW TWO SHAPES ARE SIMILAR:

• You can use the similarity statement to:1. Identify Corresponding Parts2. Create proportions3. Determine congruent angles

Correct!

Incorrect!

IF YOU KNOW TWO SHAPES ARE SIMILAR:

• You can use the similarity statement to:1. Identify Corresponding Parts2. Create proportions3. Determine congruent angles

Correct!

Incorrect!

IF YOU KNOW TWO SHAPES ARE SIMILAR:

• You can use the similarity statement to:1. Identify Corresponding Parts2. Create proportions3. Determine congruent angles

Next

IF YOU KNOW TWO SHAPES ARE SIMILAR:

• You can use the similarity statement to:1. Identify Corresponding Parts2. Create proportions3. Determine congruent angles

1

2

3

IN ORDER TO SHOW TWO FIGURES ARE SIMILAR

• You need to:1. Identify Corresponding parts2. Create Proportions3. Identify Congruent Angles • Using one of the

following “structures”i. AAii. SASiii. 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?