Given: ΔABC Prove: The sum of the interior angle measures of ΔABC is 180°.

Statement

Reason

1. Let points A, B, and C form a
triangle.

given

2. Let be a line passing
through B, parallel to ,
with angles as labeled.

defining a parallel line and labeling angles

3.

4. m∠1 = m∠4, and
m∠3 = m∠5.

Congruent angles have equal measures.

5. m∠4 + m∠2 + m∠5 = 180°

angle addition and definition of a straight angle

6. m∠1 + m∠2 + m∠3 = 180°

substitution

What is the missing step in this proof?

A.
Statement: ∠4 ≅ ∠5, and ∠1 ≅ ∠3.
Reason: Alternate Interior Angles Theorem

B.
Statement: is parallel to .

Reason: is a transversal cutting and .

C.
Statement: ∠1 ≅ ∠4, and ∠3 ≅ ∠5.

Reason: Alternate Interior Angles Theorem

D.
Statement: ∠1 ≅ ∠4, and ∠3 ≅ ∠5.
Reason: ∠1 and ∠4, and ∠3 and ∠5 are pairs of supplementary angles.

What is the ratio of the change in y-values to the change in x-values for this function? a) 1: 13 b) 2: 5 c) 5: 2 d) 13: 1

Simplify this expression.2(10) + 2(x – 4) a. 2x + 16 b. x + 12 c. 2x + 12 d. x + 16

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?