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CONGRUENCE VERSUS SIMILARITY • QUESTIONS: • If you look you are standing directly in front of a mirror looking at your image what differences do you see if any? • Is it the same as what’s actually there? • Does the size or shape change? • What about a 4 x 6 photo of yourself? • Is it the same as what’s actually there? • Does the size or shape change? • The differences between your responses can easily be explained with similarity and congruence. CONGRUENCE AND SIMILARITY CONGRUENCE https://learnzillion.com/lesson_plans/6426-identify-congruent-figures • Congruence is defined as exactly equal in size and shape. and angles are equal. • Let’s look at an example. This means all sides Let’s determine if triangle ABC is congruent to triangle A’B’C’. To do this we need to determine if the points, sides, and angles are exactly same. AB = 4 BC = 5 AC = 3 A = 90o B = 35o C = 55o A’B’ = 4 B’C’ = 5 A’C’ = 3 A’ = 90o B’ = 35o C’ = 55o What transformation took place? CONGRUENCE • Let’s look at other examples. Are the following two figures congruent? Show proof of your determination. CONGRUENCE SIMILARITY • Similarity is defined as having the same shape, having proportional corresponding sides, and corresponding angles that are equal • When two polygons are similar, we can write a similarity statement using the symbol “~” SIMILARITY • Similarity can be determined by finding the scale factor used to make the dilation. • If the same scale factor is used for each side, it is the EXACT same shape, AND all corresponding angles are congruent, then the figures are similar. • Let’s try other examples.