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QuestionMathematics

True or false: Isosceles triangles can be acute or obtuse.
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Answer

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Step 1:
I'll solve this problem step by step:

Step 2:
: Understand the definition of an isosceles triangle

An isosceles triangle is a triangle with two sides of equal length. This means two of its sides are congruent.

Step 3:
: Recall the types of triangles based on angle measurements

- Acute triangle: All interior angles are less than 90° - Obtuse triangle: One interior angle is greater than 90° - Right triangle: One interior angle is exactly 90°

Step 4:
: Analyze the possibility of angle types in an isosceles triangle

In an isosceles triangle, the two base angles (the angles opposite the equal sides) are always congruent. This means the triangle can have different angle configurations.

Step 5:
: Consider possible angle scenarios

- If the two base angles are acute (< 90°), the triangle is an acute isosceles triangle - If the vertex angle is obtuse (> 90°), the triangle is an obtuse isosceles triangle

Step 6:
: Provide a conclusive answer

Since an isosceles triangle can have either acute base angles or an obtuse vertex angle, the statement is true.

Final Answer

Isosceles triangles can indeed be acute or obtuse.