1. What are Congruent and Similar figures?
Chapter 6
Day 2
What are Congruent and Similar figures?
How are they related to Transformations?

2. Congruent Figures

3. What are Congruent Figures?
Are figures that have the exact same shape AND size!
Why learn about Congruent Figures?
Let’s see…

4. You see congruency in Architecture!
World Trade Center

5. Congruency in Architecture! Petronas Twin Towers (Malaysia’s version)
Tower One is currently being occupied by PETRONAS, the state-owned petroleum
corporation. Tower Two is being occupied by PETRONAS' associate companies
(sister companies) while the remaining space is being leased out to multinationals.
The 88-storey PETRONAS Twin Towers, developed as an integral part of the
Kuala Lumpur City Centre (KLCC) project, house PETRONAS' new corporate headquarters.
Height World Trade Center  1,368 ft
Height Petrona Twin Towers  1,483 ft (world’s tallest twin towers!)
Petronas Twin Towers (Malaysia’s version)

6. Whose Twin Towers are TALLEST? Anyone have a guess?
Height World Trade Center  1,368 ft
Height Petrona Twin Towers  1,483 ft (world’s tallest twin towers!)
Twin Towers – New York Twin Towers - Malaysia

7. Congruency in Architecture!
Huge dispute in Portland. Many citizens felt that the mayor of Portland spent
way too much of the tax payers money to add what they considered just a
decoration to make the convention center pretty.
Portland, Maine Convention Center and Hotel

8. The US Department of Treasury must use congruency when it makes money!
The U.S. Treasury Department uses congruency when it makes money.
What would happen if the bill and coins were not congruent?
Would these vending machines work if they were not congruent?
NO they would not work!

9. Manufacturers use congruency when making their products!
Assembly Line
Packaging
Apple
City Shopper Barbie
Manufactures use congruency when they make their products. The phones may be different colors, but they are exactly the same shape and size! The same with the toys. In order to pack these items each must be made exactly the same or they will not fit in the packing!
Toy Makers

11. Corresponding Parts of Congruent Figures
Triangle ABC
Triangle DEF

12. How do TRANSFORMATIONS relate to CONGRUENCY?
Transformations that translate (slide), reflect (flip), and rotate (turn)
a figure do not change its size or shape.
Translations, reflections, and rotations ONLY change the position and orientation of a figure.
Therefore, the figure and its image are congruent.
Translation
Reflection
Rotation
congruent
congruent
congruent
So… this being said
If two figures are congruent, then a transformation (or series of transformations) will MAP one figure onto the other.

13. Similar Figures

14. What are Similar Figures?
Are figures that have the exact same shape BUT
are a different size!
What does similarity look like in nature?
Let’s see…

15. Similarity in Families

16. Similarity in the Animal Kingdom

18. Which is the preimage and which is the image? How do you know?
These two triangles are similar, because their ANGLE measurements are the SAME, but their SIDE lengths are DIFFERENT.
The smaller triangle is the image because it has the prime symbols.
Which is the preimage and which is the image? How do you know?

19. How do TRANSFORMATIONS relate to SIMILARITY?
A dilation is a transformation in which a figure and its image are similar.
Dilation
Similar
Angles are the same
Different side lengths

20. Time for Classwork

21. End of PowerPoint