Suppose you decide to throw a birthday party for your best friend. One of the items on your list of things to do is to make or buy a cake. If you expect to have more than just a few people at the party, you'll probably need to order a sheet cake rather than a round layered cake.
You only have a certain amount of money, and you purchase the largest sheet cake you can afford, hoping it will be enough for all the guests to enjoy a piece. Next you need to decide how to divide up the cake. After the candles and the birthday song, do you cut the cake into rectangular pieces that are all the same size, or do you ask each guest what size piece he or she would like?
Thinking about congruent and similar shapes can help you decide on the best approach to serving a limited amount of cake. Which of these images shows a cake cut into congruent rather than similar pieces? Click that image to see if you remember the difference.
Now think about the effect that each set of shapes will have on your cake-serving experience at the party. Which approach will help you make sure that you have enough cake for everyone?
Congruent figures are exactly the same size and shape. Similar figures, while the same shape, are not the same size. If you decide to cut the cake into congruent pieces, you can figure out what size all the pieces need to be to provide a piece for each person at the party. Be sure to count your guests before you begin slicing!
If you allow your guests to choose their own size slice, you will have similar but not congruent pieces of cake. Since not all the slices will be the same size, it will be very hard to predict or control if you have enough cake for everyone.
