construct an isosceles triangle and construct Sierpinksi's triangle. Repeat the pattern three times. What segment of a triangle does this pattern make use of over and over again?
To construct an isosceles triangle, follow these steps:
1. Start by drawing a straight line segment. This will be the base of your triangle.
2. From one endpoint of the base, use a compass to draw an arc that intersects the base.
3. Keeping the compass width the same, place the compass point on the other endpoint of the base and draw another arc that intersects the base. The intersection point of these two arcs will be the third vertex of the triangle.
4. Use a ruler to connect this vertex with the endpoints of the base, creating the two equal sides of the isosceles triangle.
To construct Sierpinski's triangle and repeat the pattern three times, follow these steps:
1. Start by drawing an equilateral triangle. This will be the base triangle of the pattern.
2. Divide the base triangle into four congruent smaller equilateral triangles by drawing lines connecting the midpoints of each side to the opposite vertex.
3. Erase the inner upside-down equilateral triangle in the center.
4. Repeat the previous steps on each of the remaining three equilateral triangles, making sure to divide them into more smaller equilateral triangles and erasing the inner triangles.
5. Repeat this process a total of three times, resulting in a Sierpinski's triangle with several smaller triangles.
The pattern in Sierpinski's triangle makes use of the repeated division of equilateral triangles into four smaller equilateral triangles. This specific pattern continuously uses and repeats the segment connecting the midpoints of the sides of the equilateral triangle.
geez. Just look at the diagram. It should be clear what part of the triangle is used. No idea at all?
And sorry, can't do constructions here. I'm sure google can help out though.