Question

The angle measures and/or side lengths of a triangle are described. Determine whether the conditions given determine a unique triangle, determine more than 1 triangle, or cannot make a triangle.

4 in., 5 in., 50(degrees), arranged in listed order

Answer 1

Recall and apply triangle properties.Sketch and construct triangles with given conditions.Determine whether a set of given conditions for the measures of angle and/or sides of a triangle describe a unique triangle, more than one possible triangle or do not describe a possible triangle.

Answer 2

The conditions you listed can be abbreviated "Side-Side-Angle",
or "S-S-A".

In the geometry you've had so far, have you ever seen this as
a condition for defining a triangle, or for saying that two triangles
are congruent ?

It isn't because it doesn't define a unique triangle.

It WOULD, if the angle were between the two sides (S-A-S).
But with the angle out on the end of the two sides, it doesn't
nail the triangle down.

You can make an infinite number of different triangles with
two adjacent sides of 4 and 5, and a 50° angle out at the end.

(One of them is a right triangle, with legs of 3 and 4, and
the hypotenuse 5 units long. With that one crossed off
of the list, there are only an infinite number of others.)