Vivian found the lcm of 3 and 6. her work is shown here. multiples of 3: 3, 6, 9, 12, 15, . . multiples of 6: 6, 12, 18, 24, 30, . . the lcm is 12. what was vivian’s error? the student needed to list more multiples for each number. the student listed factors of each number instead of multiples. the student should have multiplied 3 and 6 to find the lcm. the student selected a multiple that is not the least of the common multiples.

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