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The difference between a triangle and a triangular region lies in their definitions and conceptualizations:

1. Triangle:

   • A triangle is a geometric figure formed by three line segments called sides, and three angles.
   • It is defined by connecting three non-collinear points in a plane.
   • Each side of the triangle connects two vertices, and each vertex is a point where two sides intersect.
   • A triangle is a two-dimensional shape with no interior space.

2. Triangular Region:

   • The triangular region refers to the interior space enclosed by the sides of a triangle.
   • It is the area bounded by the three sides of the triangle.
   • The triangular region is the two-dimensional space within the triangle itself.
   • It includes all the points that lie inside the triangle, including the area enclosed by the sides and the vertices of the triangle.

In summary, a triangle is the geometric figure formed by three line segments, while the triangular region is the area enclosed by those line segments within the triangle. The triangle itself represents the boundaries of the triangular region.

To draw triangle DEF with side lengths DE = DF = 4 cm and EF = 6 cm, follow these steps:

1. Draw a line segment of length 6 cm. This will represent side EF.

2. At one end of the line segment, mark point F.

3. With F as the center and a radius of 4 cm, draw an arc to intersect the line segment EF. Mark this point as D.

4. Now, with F as the center and a radius of 4 cm, draw another arc to intersect the line segment EF. Mark this point as E.

5. Connect points D, E, and F to form triangle DEF.

Now, to measure angles E and F, you can use a protractor:

• Measure angle E: Place the center of the protractor at point E, align the baseline of the protractor along side DE, and read the angle where side EF intersects the protractor.

• Measure angle F: Place the center of the protractor at point F, align the baseline of the protractor along side EF, and read the angle where side DE intersects the protractor.

For an isosceles triangle, the line of symmetry can also be referred to as the "axis of symmetry." This line divides the triangle into two mirror-image parts, running from the apex (the vertex opposite the base) to the midpoint of the base.

Shapes with no line of symmetry do not divide into two mirror-image halves, regardless of how you try to fold or bisect them. Here are three examples:

1. Scalene Triangle: A triangle with all sides of different lengths and all angles of different sizes has no line of symmetry because there is no way to divide it into two parts that are mirror images of each other.

2. Irregular Polygon: An irregular polygon, which does not have equal-length sides or equal angles, typically has no line of symmetry. An example would be a five-sided polygon where no two sides or angles are the same.

3. Parallelogram (excluding rectangles and rhombuses): A general parallelogram (which is not a rectangle or rhombus) has no lines of symmetry. Its opposite sides are equal in length, and opposite angles are equal, but it does not fold into two parts that are mirror images of each other unless it is a special type like a rectangle or rhombus, which do have lines of symmetry.

These shapes illustrate that symmetry is not a universal characteristic of all geometric figures.

So, the area of the square is 272.25 square meters.

So, the area of the rectangular field is approximately 6.18 acres.

First, let's find the distance around the field, which is the perimeter of the rectangle:

Perimeter of the rectangle = 2 × (Length + Width) = 2 × (290 m + 210 m) = 2 × 500 m = 1000 m

Now, let's find the time it takes for the girl to go two times around the field:

Distance covered = 2 × Perimeter of the field = 2 × 1000 m = 2000 m

Given that the girl walks at the rate of 1.5 m/sec, we can use the formula:

Time = Distance / Speed

Time = 2000 m / 1.5 m/sec ≈ 1333.33 sec

So, it will take approximately 1333.33 seconds for the girl to go two times around the field.