8.5+INDIRECT+MEASYREMENT+AND+ADDITIONAL++SIMILARITY+THEOREMS.+T&amp;A

OBJECTIVES: 1. Use triangle similarity to measure distances indirectly. 2. Develope and use similarity theorems for altitudes and medians of triangles.


 * __DEFINITIONS AND BLUE BOXES:__

PROPORTIONAL ALTITUDES THEOREM-** If two triangles are similar, then corresponding altitudes have the same ratio as their corresponding sides. their correspondig median have the same tatio as theri corresponding sides. their corresponding angle bisectors have the same ratio as the corresponding sides. the opposite side into two segments that have the same ratio as the other two sides.
 * PROPRTIONAL MEDIANS THEOREM-** If two trinagles are similar, then
 * PROPORTIONAL ANGLE BISECTORS THEOREM-** If two triangles are similar,
 * PROPORTIONAL SEGMENTS THEOREM-** An angle bisector of a triangle divides

Our example is a person playing basketball and a hoop and we are trying to find the height of the hoop. First you have to know how tall the person and in this example is 69 inches and you have to know the length of the shadow and in this case it is 55 inches. Then you have to know the length of the shadow on the hoop, and that is 86 inches and the height is what we are trying to find and that is X. so you put X over 69 and then you put 86 over 55. Then you divide 86 over 55 and that is, then you multiply that by 69 and that is 107 inches. So then you take 107 and divide that by 12 because there is 12 inches in a foot and that comes out to be 8 feet 9 inches tall.
 * EXAMPLES:**