In ΔABC shown below, segment DE is parallel to segment AC : The following two-column proof with missing statements and reasons proves that if a line parallel to one side of a triangle also intersects the other two sides, the line divides the sides proportionally:

Which statement and reason accurately completes the proof? (5 points)

a
4. ΔBDE ∼ ΔBAC; Side-Angle-Side (SAS) Similarity Postulate
5. ∠B ≅ ∠B; Reflexive Property of Equality

b
4. ∠B ≅ ∠B; Reflexive Property of Equality
5. ΔBDE ∼ ΔBAC; Angle-Angle (AA) Similarity Postulate

c
4. ΔBDE ∼ ΔBAC; Side-Angle-Side (SAS) Similarity Postulate
5. ∠A ≅ ∠C; Isosceles Triangle Theorem

d
4. ∠A ≅ ∠C; Isosceles Triangle Theorem
5. ΔBDE ∼ ΔBAC; Angle-Angle (AA) Similarity Postulate

A, b, c, and d have the coordinates (-8, 1), (-2, 4), (-3, -1), and (-6, 5), respectively. which sentence about the points is true? a. a, b, c, and d lie on the same line. b. and are perpendicular lines. c. and are parallel lines. d. and are intersecting lines but are not perpendicular. e. and are parallel lines.

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?

Which function in vertex form is equivalent to f(x) = x2 + 6x + 3? f(x) = (x + 3)2 + 3 f(x) = (x + 3)2 − 6 f(x) = (x + 6)2 + 3 f(x) = (x + 6)2 − 6