Given: AB ≅ CD and AD ≅ BC Prove: ABCD is a parallelogram. Quadrilateral A B C D is shown. A diagonal is drawn from point A to point C. Sides A B and D C are congruent. Sides A D and B C are congruent. 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

High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. because the number of slots remains relatively stable, some colleges reject more early applicants. suppose that for a recent admissions class, an ivy league college received 2851 applications for early admission. of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. in the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375. let e, r, and d represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool.suppose a student applies for early admission. what is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process?