Question

How many triangles can you make with two side lengths of 6 inches that meet at a 50 degree angle.

Answer 1

Answer: Exactly One Triangle

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Explanation:

Recall that by the SAS (side angle side) congruence theorem, if we know that two pairs of sides are the same length and the angles between them are also congruent, then we can conclude the triangles are congruent. This further means that we can only construct exactly one triangle with two side lengths of 6 inches, and they form a 50 degree angle between them. Applying transformations such as rotations, translations, or reflections will not change the triangle.

Side note: This triangle is isosceles because two sides are the same length. It is not equilateral because we would need to have all three angles to be 60 degrees.

Answer 2

Answer:

One triangle only

Step-by-step explanation: