How many unique triangles can be drawn with side lengths 12 cm and 16 cm, and a 50° included angle? A. 0
B. 1
C. 2
D. an infinite number

ANSWER:

1 unique triangle

Step-by-step explanation:
There are several ways to determine if the information given about a triangle produces a unique triangle or not. One option is to provide two side lengths and the angle included between them, this is known as SAS (side-angle-side) congruence, this is not to be confused with SSA (side-side-angle) congruence. Since this is one of the groups of givens that provides a unique triangle, then the number of unique triangles that can be drawn is 1 unique triangle.

c) 6

step-by-step explanation:

let pq = qr = rs = x, and xz = y and zu = z.

if the horizontal lines are parallel, then corresponding segments are in proportion:

substitute:

therefore 3 = y = z.

xu = y + z → xu = 3 + 3 = 6