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Chapter 5: Problem 57

Determine whether the statement is true or false. Justify your answer. If a triangle contains an obtuse angle, then it must be oblique.

Short Answer

Expert verified
The statement is true. A triangle with an obtuse angle cannot be a right triangle, therefore it must be an oblique triangle.

Step by step solution

01

Understanding basic definitions

First, it's important to understand what an obtuse angle and an oblique triangle are. By definition, an obtuse angle is an angle that is greater than 90 degrees and less than 180 degrees. An oblique triangle, meanwhile, is any triangle that does not contain a right angle, i.e., an angle of 90 degrees.
02

Analyzing the statement

The given statement is saying that any triangle with an obtuse angle must be oblique, that is, not a right triangle. Given our understanding of the definitions from Step 1, we can see that a triangle with an obtuse angle indeed cannot be a right triangle, because a right triangle requires a 90 degree angle, and having an obtuse angle (over 90 degrees) would contradict that.
03

Drawing conclusions

Based on the definitions of obtuse angle and oblique triangle, as well as the analysis of the statement made in the previous steps, it can be concluded that the statement 'If a triangle contains an obtuse angle, then it must be oblique' is true. Having an obtuse angle precludes a triangle from being a right triangle, thereby making it an oblique triangle by definition.

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