What are Congruence and Similarity?
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Basics on the topic What are Congruence and Similarity?
What are congruence and similarity? This video explores the definitions of these two terms and how we can identify objects as either similar or congruent.
Transcript What are Congruence and Similarity?
Luis is planning a game night with his friend, Kai to play Shape Shift Quest. But, he realizes he is missing some pieces for the game and decides to give his new 3D printer a go at replacing them. In order to do that he needs to answer the question: 'What are congruence and similarity?' Congruent means that two figures are the exact same shape and size. They also have the same side lengths and angle measurements. Similar means that two figures are the same shape, but they are different sizes Similar figures do not have the same side lengths, but they do have the same angle measurements. Luis is ready to compare the first piece he printed. Are these two figures similar or congruent? They are the same shape, but because it is a different size, these pieces are similar. Luis adjusts some measurements and copies the game piece again. Are these two figures similar or congruent? Again, the game piece is the same shape, but because it is larger, it is similar. What type of changes does Luis need to make for the game piece to be congruent? Remember, to have a congruent figure, it needs to be the same shape and the same size. Are these two figures similar or congruent? He is successful! The game piece he created is the same shape and the same size, so it's congruent. Game night is approaching quickly, and Luis has one more missing triangular game piece to recreate. After it's done, he realizes that the piece has the same angle measurements, but the lengths are different. Pause the video here and determine if these triangles are similar or congruent and why. These triangles are similar because they have the same angle measurements, but different side lengths. A way to show that figures have the same angle measurements is to use matching 'arcs' on the angles. Here's Luis' next piece. Pause the video to determine whether these two figures are similar or congruent. These two shapes are similar again because they have the same angle size but the new game piece has shorter side lengths. Luis is running out of time and tries one last time to make the missing piece. How did he do? Pause the video here and decide, are these similar or congruent? They are the same! Since the corresponding angles are equal, as well as the side lengths, these two figures are congruent. Luis and Kai are ready for a match-up for board game night! Remember in order for two figures to be congruent, they must have the exact same angles and side lengths and are a copy of each other. If they are the same shape but have different sizes, they are similar. It looks like Luis is going to need to teach Kai all he knows about congruency versus similarity!
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What are Congruence and Similarity?