Triangle a b c is shown. lines are drawn from each point to the opposite side and intersect at point d. they form line segments a g, b e, and c f. in the diagram, which must be true for point d to be an orthocenter? be, cf, and ag are angle bisectors. be ⊥ ac, ag ⊥ bc, and cf ⊥ ab. be bisects ac, cf bisects ab, and ag bisects bc. be is a perpendicular bisector of ac, cf is a perpendicular bisector of ab, and ag is a perpendicular bisector of bc.

step-by-step explanation:

if segment d is connected to the objective of a the answer would be d-a would give u b

therefore, the answer is b.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for