Question

identifying dimensions that create two triangles
which dimensions will create an unlimited number of triangles?
angle 55°
angle 50°
angle 60°
side length of 6 in.
side length of 8 in.
side length of 10 in.
angle 45°
angle 45°
angle 90°
side length of 5 in.
side length of 10 in.
side length of 12 in.

Explanation:

Step1: Check triangle angle sum

The sum of angles in a triangle is \(180^{\circ}\). For the first set \(55 + 50+60=165
eq180\). For the third set \(45 + 45+90 = 180\). But when we consider triangle construction, if we know three angles (AAA - Angle - Angle - Angle), the triangles are similar (same shape but can have different sizes). So, there are infinitely - many triangles (scaled versions of each other).
For the side - side - side (SSS) cases (second and fourth options), by the SSS congruence criterion, only one unique triangle (up to congruence) can be formed.

Answer:

The dimensions with angles \(45^{\circ}\), \(45^{\circ}\), \(90^{\circ}\) will create an unlimited number of triangles.