8.2+SIMILAR+POLYGONS.+T&A

OBJECTIVES: 1. Define similar polygons. 2. Use properties of proportions and scale factors to solve problems involving similar polygons.


 * DEFINITIONS AND BLUE BOXES:**

image of the other by a dilation. a way of setting up a correspondece between their sides and angles such athat the following conditions are met: Each pair of corresponding andles is congruent. Each pair of corresponding sides is proportional. Let a, b, c, and d be any real numbers. ad=bc. b/a = d/c. a/c = b/d a+b/b = c+d/d.
 * SIMILAR FIGURES** - Two figures are similar if and only if one is congruent to the
 * POLYGON SIMILARITY POSTULATE** -Two polygons are similar if and only if there is
 * PROPERTIES OF PROPORTIONS-**
 * CROSS-MULTIPLICATION PROPERTY -** if a/b = c/d and d is congrunent to 0 then
 * RECIPROCAL PROPERTY -** if a/b = c/d and a, b, c, and d are congruent to 0 then
 * EXCHANGE PROPERTY -** If a/b = c/d and a, b, c, and d is congruent to 0 then
 * "ADD-ONE" PROPERTY-** If a/b = c/d and b and d is congruent to 0 then

If you have 2 triangles and you are trying to prove that they are similar. First you have to know the numbers on the sides, in this case we have two triangles and the numbers are for the first one 16, 23, and 36, for the second one they are 7, 17, and the third number is missing which is X. If they dont give you all dementions like in this problem you have to find it. You take the numbers 17 over 23 and x over 36 and you cross multiply. You take 36 * 17 and that is 612 and then you divide that by 23 and that equals 36. Thats only the first part of the problem the second part of the problem is that you take the two smallest sides and divide those and then you take the next two smallest sides and divide those two and then you take the biggest two and divide those two. If they all equal the same fraction then the triangles are similar, in this case they are not similar because 36 over 36 is 1 and 7 over 16 is .4375 and 17 over 23 is .7391304
 * EXAMPLE:**