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Mathematics

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You're right, my apologies for the cut-off! Let's tackle this new question.

Here are the types of triangles and their axes of symmetry:

  • 1. The triangle has sides of lengths 3 cm3 \text{ cm}, 3 cm3 \text{ cm}, and 3 cm3 \text{ cm}. Since all three sides are equal, it is an equilateral triangle. An equilateral triangle has 3 axes of symmetry. Each axis passes through a vertex and the midpoint of the opposite side.

  • 2. The triangle has sides of lengths 2 cm2 \text{ cm}, 4 cm4 \text{ cm}, and 5 cm5 \text{ cm}. Since all three sides are of different lengths, it is a scalene triangle. A scalene triangle has no axes of symmetry.

  • 3. The triangle has sides of lengths 6 cm6 \text{ cm}, 8 cm8 \text{ cm}, and 6 cm6 \text{ cm}. Since two sides are equal (6 cm6 \text{ cm} and 6 cm6 \text{ cm}), it is an isosceles triangle. An isosceles triangle has 1 axis of symmetry. This axis passes through the vertex between the two equal sides and the midpoint of the base (8 cm8 \text{ cm} side).

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