Question

Drag a statement or reason to each box to complete this proof. Given: m(acd) = 60. Prove: ABC is an obtuse triangle.

Answer 1

To show that triangle ABC is an obtuse triangle with a given angle m(∠ACD) = 60 degrees, we reason that ∠ACB must be greater than 90 degrees since the sum of angles in a triangle is 180 degrees. This general proof relies on the exterior angle theorem and the definition of an obtuse triangle.

Step-by-step explanation:

To complete the proof that triangle ABC is an obtuse triangle, given that m(∠ACD) = 60 degrees, we first must understand the relationship between the angles of a triangle and how they define the type of triangle. An obtuse triangle has one angle greater than 90 degrees. Based on the given information and additional assumptions made from the provided geometrical relationships, it appears there may be some typographical error or missing context; nevertheless, we can theorize a basic proof:

1. Recognize that the sum of angles in a triangle equals 180 degrees.
2. Since ∠ACD = 60 degrees, then ∠ACB must be greater than 90 degrees to satisfy the given condition of ABC being an obtuse triangle (as ∠ACD is an exterior angle to triangle ABC).
3. Thus, triangle ABC must have an angle ∠ACB greater than 90 degrees, making it an obtuse triangle.

Note that due to missing details, the above steps are a generalized approach and may not reflect the specific information provided originally.