Worksheets for learning the properties of 2D shapes.

The task involves identifying and writing down the properties of 2D shapes. Below, I will explain the solution for each shape mentioned in the image.

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Properties of a Square

A square is a type of quadrilateral (a polygon with four sides). Here are its key properties:
1. All sides are equal in length.
2. All interior angles are right angles (90°).
3. Opposite sides are parallel.
4. Diagonals are equal in length.
5. Diagonals bisect each other at right angles (90°).
6. Diagonals bisect the angles of the square.
7. It has rotational symmetry of order 4 (it looks the same after a rotation of 90°, 180°, 270°, and 360°).
8. It has reflectional symmetry along both diagonals and both pairs of opposite sides.

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Properties of a Triangle

A triangle is a polygon with three sides. The properties depend on the type of triangle (e.g., equilateral, isosceles, scalene), but here are the general properties:
1. It has three sides and three angles.
2. The sum of the interior angles is always 180°.
3. The length of any side must be less than the sum of the lengths of the other two sides (triangle inequality theorem).
4. Depending on the type:
- Equilateral triangle: All sides are equal, and all angles are 60°.
- Isosceles triangle: Two sides are equal, and the angles opposite those sides are also equal.
- Scalene triangle: All sides and angles are different.
5. It has rotational symmetry of order 3 if it is an equilateral triangle.
6. It has reflectional symmetry depending on the type:
- Equilateral triangle: Symmetry along three axes.
- Isosceles triangle: Symmetry along one axis.
- Scalene triangle: No symmetry.

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Solution Summary

Here is how you can write the answers:

#### For the Square:
- All sides are equal.
- All angles are 90°.
- Opposite sides are parallel.
- Diagonals are equal and bisect each other at 90°.
- Diagonals bisect the angles.
- Rotational symmetry of order 4.
- Reflectional symmetry along diagonals and sides.

#### For the Triangle:
- Three sides and three angles.
- Sum of interior angles is 180°.
- Sides follow the triangle inequality theorem.
- Types include equilateral (all sides equal, all angles 60°), isosceles (two sides equal, two angles equal), and scalene (all sides and angles different).
- Equilateral triangle has rotational symmetry of order 3.
- Symmetry depends on the type: equilateral (three axes), isosceles (one axis), scalene (no symmetry).

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Final Answer

\[
\boxed{
\text{Square: All sides equal, all angles 90°, opposite sides parallel, diagonals equal and bisect at 90°.}
}
\]
\[
\boxed{
\text{Triangle: Three sides, sum of angles 180°, follows triangle inequality, types include equilateral, isosceles, scalene.}
}
\]