Question

Decide if the measurements determine no triangle, a unique triangle, or more than one triangle.

ITEMBANK:
3 cm, 4 cm, 11 cm

3 cm, 5 cm, 15 cm

30°, 40°, 110°

6 cm, 7 cm, 12 cm

60°, 60°, 60°

8 cm, 90°, 45 °

Options: No triangle, Unique triangle, or More than one triangle

Answer 1

1.)No Triangle

2.)No Triangle

3.)More Than One Triangle

4.)Unique Triangle

5.)More Than One Triangle

6.)Unique Triangle

Answer 2

1) No triangle
2) No triangle
3) More than 1 triangle
4) 1 triangle
5) More than 1 triangle
6) Either 1 or more than 1 triangle

Step-by-step explanation:
1) The sum of the two smaller sides is not greater than the third side, so these will not form a triangle.
2) The sum of the two smaller sides is not greater than the third side, so these will not form a triangle.
3) The angles add up to 180, so this will make more than one triangle (there is no information given about the sides, so the triangles would be similar but not necessarily congruent)
4) The sum of the two smaller sides is greater than the third side, so one triangle is formed
5) The angles add up to 180, so this will make more than one triangle (there is no information given about the sides, so the triangles would be similar but not necessarily congruent)
6) Depending on whether the side is between the two given angles, either 1 triangle or more than 1 triangle could be formed.