The speeds of 12 particles (in cm s-1) are 0.5, 1.5, 1.8, 1.8, 1.8, 1.8, 2.0, 2.5, 2.5, 3.0, 3.5, and 4.0. Find (a) the average speed, (b) the root-mean-square speed, and (c) the most probable speed of these particles. Explain your results.

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