Draw an equilaterla triangle. Divide each side in half and join the points to make four small equilateral triangles. Rearrange these four equilateral triangles into a parallelogram. Compare the perimeter of the original triangle with the perimeter of the parallelogram. Explain your results.
It is a rectangle
To draw an equilateral triangle, follow these steps:
1. Start by drawing a straight line segment.
2. On one end of the line segment, place the tip of your compass. Set the other end of the compass on the other end of the line segment.
3. Without changing the compass width, draw an arc from each end of the line segment.
4. Keep the compass width the same and place the tip on one of the arcs. Draw an arc that intersects with the previous two arcs.
5. Repeat step 4 for the other arc.
6. Draw straight lines connecting the points where the arcs intersect.
Now that we have drawn the equilateral triangle, let's divide each side in half to create four small equilateral triangles. To do this, follow these steps:
1. Draw a straight line connecting two corners of the equilateral triangle, cutting it in half.
2. Repeat step 1 for the other two sides of the triangle.
After dividing each side in half, you will have four smaller equilateral triangles within the original triangle.
Next, let's rearrange these four equilateral triangles into a parallelogram. To do this, follow these steps:
1. Take one of the smaller equilateral triangles and place it adjacent to the original triangle.
2. Align the sides of the triangles so that they touch and form a straight line.
3. Repeat this step for the other three smaller triangles until they form a parallelogram.
Comparing the perimeter of the original triangle with the perimeter of the parallelogram, we can observe the following:
- The perimeter of the original equilateral triangle can be calculated by multiplying the length of one side by 3, as all sides of an equilateral triangle are equal.
- The perimeter of the parallelogram can be calculated by adding the lengths of its four sides.
Since the four smaller equilateral triangles were formed by dividing each side of the original triangle in half, the perimeter of the parallelogram should be twice the perimeter of the original triangle.
Therefore, by comparing the perimeters, we conclude that the perimeter of the parallelogram will be twice the perimeter of the original equilateral triangle.