Question

Each of the conditions below create different numbers of triangles. Match the conditions based on the number of triangles the conditions create. Assume inches are the only units used. PLEASE HELP!!

Answer 1

• 1 -- C
• 2 -- A
• 3 -- B
• 4 -- E

Explanation:

A: 2 given sides and the given angle between them will produce 1 triangle.

B: The sum of angle is 190°. 0 triangles are possible.

C: An infinite number of triangles can have the given base and height.

D: The remaining side must be from the set {3, 4, 5}. 3 triangles are possible.

E: Leg lengths can be from the set {(2, 2), (2, 4), (2, 6), (2, 8), (4, 4)}. 5 triangles are possible.

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1: An infinite number of triangles can have those angle measures.

2: The remaining side must have length 2. 1 triangle is possible.

3: The perimeter constrains the remaining side length to a value too short to form a triangle. 0 triangles are possible.

4: The remaining side length must be from the set {1, 2, 3, 4, 5}. 5 triangles are possible.

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So, the matchups are ...

1 -- C (an infinite number)

2 -- A (1 triangle)

3 -- B (0 triangles)

4 -- E (5 triangles)