3 Consider the set X = { 1 , 2 , 3 , 4 , 5 } and suppose you have two holes. Also suppose that you have 10 pigeons: the 2 -element subsets of X . Can you put these 10 pigeons into the two holes in a way that there is no 3 -element subset S = { a , b , c } ⊂ X for which all pigeons from S go in the same hole? Then answer the same question if X = { 1 , 2 , 3 , 4 , 5 , 6 } with 15 = C ( 6 , 2 ) pigeons.

Abdul is making a map of his neighborhood he knows the following information: his home, the middle school, and high school are all on the same street. his home, the elementry school, and his friends house are on the same street. the angle between the elementary school, middle school, and his home is congruent to the angle between his friends house, the high school, and his home. what theorem can abdul use to determine the two triangles are similar? a- side side side similarity theoremb- angle angle similarity theoremc- corresponding parts of similar triangles are congruentd- pieces of right triangles similarity theorem