Select all the conditions for which it is possible to construct a triangle. A. A triangle with angle measures 60°, 80°, and 80°
B. A triangle with side lengths 4 cm, 5 cm, and 6 cm
C. A triangle with side lengths 4 cm, 5 cm, and 15 cm
D. A triangle with side lengths 4 cm and 5 cm and a 50° angle
E. A triangle with angle measures 30° and 60°, and a 3 cm side length

the aswere is the one with all 8's and the second one is with the 10,8 and 6

step-by-step explanation:

, 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

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.