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What are the properties of the various triangles given:

  • Isosceles triangles have two sides equal, two angles equal
  • Scalene triangles have all three sides different and all three angles different
  • Right triangles have one angle which is a right angle (90°)
  • acute triangles have all angles less than 90°
  • obtuse triangles have one angle greater than 90°

As an isosceles triangle has two sides equal, it cannot be a scale triangle which has all three angles different.

For the other three properties, consider:

The sum of the angles in a triangle is 180°

If one angle is 90°, the other two angles could be: (180° - 90°) / 2 = 45° each - two angles the same

→ an isosceles triangle could be a right triangle

If all angles are less than 90°, let one angle be 80°, the other two angles could be: (180° - 80°) / 2 = 50° each - two angles the same

→ an isosceles triangle could be an acute triangle

(Note that if one angle was 60°, then the other two being equal would be: (180° - 60°) / 2 = 60° each making all three angles the same and the triangle an equilateral triangle)

If one angle is greater than 90°, let it be 100°, the other two angles could be: (180° - 100°) / 2 = 40° each - two angles the same

→ an isosceles triangle could be an obtuse triangle

From the given list, an isosceles triangle could be a right, acute or obtuse triangle, but it could not be a scalene triangle.

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Q: What type of triangle can an isosceles triangle be scalene right acute obtuse?
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