If the sides of this square are increased by 1 inch each, how would the perimeter change? What would it change to?

In trapezoid abcd, ac is a diagonal and ∠abc≅∠acd. find ac if the lengths of the bases bc and ad are 12m and 27m respectively.

Given: ab ≅ cd and ad ≅ bc prove: abcd is a parallelogram. statements reasons 1. ab ≅ cd; ad ≅ bc 1. given 2. ac ≅ ac 2. reflexive property 3. △adc ≅ △cba 3. ? 4. ∠dac ≅ ∠bca; ∠acd ≅ ∠cab 4. cpctc 5. ∠dac and ∠bca are alt. int. ∠s; ∠acd and ∠cab are alt. int. ∠s 5. definition of alternate interior angles 6. ab ∥ cd; ad ∥ bc 6. converse of the alternate interior angles theorem 7. abcd is a parallelogram 7. definition of parallelogram what is the missing reason in step 3? triangle angle sum theorem sas congruency theorem sss congruency theorem cpctc

In a class of 77, there are 44 students who play soccer. if the teacher chooses 33 students, what is the probability that none of the three of them play soccer?