Drag each condition to the correct location on the table. Match each condition to the number of triangles that can be constructed to fit the condition. condition A: one side measuring 4 inches, another side measuring 8 inches, and a third side measuring 10 inches condition B: one angle measuring 60°, another angle measuring 40°, and a third angle measuring 90° condition C: one side measuring 4 inches, another side measuring 8 inches, and the angle between them measuring 70° condition D: one side measuring 5 inches, another side measuring 7 inches, and a third side measuring 12 inches condition E: one angle measuring 30°, another angle measuring 80°, and the length of the included side measuring 8 inches condition F: one angle measuring 40°, another angle measuring 80°, and a third angle measuring 60°

No triangles are possible for Options B and D. One triangle is possible for options A, C, and E. Many triangles are possible for option F.

How to interpret Triangles?

For it to be a triangle, then it must have 3 vertices and 3 sides with the sum of 2 sides greater than the third side. Also, the sum of interior angles must be 180°.

A) Side lengths of the triangle are; 4 inches, 8 inches and 10 inches.

4 + 8 > 10. Thus, it is a triangle.

B) 60° + 40° + 90° = 190 ≠ 180°

Thus, no triangle is possible because the sum of the angles in triangle is 180°.

C) There are two sides are given and one angle. Thus, from SAS congruency theorem, one triangle is possible.

D) 7 + 5 = 12

There is no triangle possible because the sum of the two sides must be greater than the third side.

E) We are given two angles and one side. Thus, from the ASA Congruency Postulate, one triangle is possible.

F) 60° + 80° + 40° = 180°

There are three angles given, but no sides and so we can say that many triangles are possible.

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