Obtuse Triangle Practice

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Question 1
Which of the following triangles are obtuse triangles?

identify all the obtuse triangles

Answer

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A. I & II
B. II & III
C. III & IV
D. I & IV
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Step by Step Solution 

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Step 1
For triangle I, there is no internal angle that is >90°. Hence, this is not an obtuse triangle.
Triangle I is not an obtuse triangle
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Step 2
As for triangle II, it is not an obtuse triangle for the same reason as above.
Triangle II is not an obtuse triangle
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Step 3
As for triangle III, the angle at vertex A is >90°. Hence, it is an obtuse triangle.
Triangle III is an obtuse triangle
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Step 4
For triangle IV, it is an obtuse triangle because the angle at vertex C is >90°
Triangle IV is an obtuse triangle
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Step 5
Clearly, only triangle III and IV are obtuse triangles. Therefore, the answer is C.
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