Step 9
Measure the length of one side of the triangle using a ruler. Let's say it is 5 centimeters.
Step 10
Use a compass to mark the midpoint of each side of the triangle. To do this, place the needle of the compass on one vertex of the triangle and set the compass to half the length of the side. Draw an arc that intersects the side of the triangle. Repeat this process for the other two sides of the triangle.
Step 11
Use a straightedge to connect the midpoints of the sides of the triangle. You should now have a smaller equilateral triangle inside the original triangle.
Step 12
Check your work by measuring the length of one side of the inner triangle using a ruler. It should be half the length of the corresponding side of the original triangle. In this case, it should be 2.5 centimeters.
Step 13
Use a compass to repeat steps 10-12 with the inner triangle. Mark the midpoints of its sides, connect them using a straightedge, and check the length of one side of the smaller inner triangle.
Step 14
Repeat steps 10-13 as many times as you want to create smaller and smaller equilateral triangles inside the previous triangles. Each inner triangle should have half the side length of the previous triangle.
Step 15
Continue the pattern until you reach your desired level of detail or until you run out of space on your paper. Each time you repeat the steps, you will be creating smaller and smaller equilateral triangles.
Step 16
Check your work by measuring the length of one side of each inner triangle. Each time, it should be half the length of the previous triangle's corresponding side.
Step 17
You should now have a fractal pattern of nested equilateral triangles on your paper. Each triangle is a reduced version of the previous one, creating a visually pleasing and mathematically intriguing design.
Step 1
Mark a point on your paper.
Step 2
Place the needle of the compass on that point and draw a circle. Make sure the whole circle fits on your piece of paper.
Step 3
Keep the compass setting. Mark a point on the circle. Label this point A. Then place the needle of the compass on that point, and draw an arc that intersects the circle. Mark that intersection point (but don't label it).
Step 4
Keep the compass setting. Place the needle of the compass on that new unlabeled point, and draw an arc that intersects the circle. Label the intersection point with the circle as point B.
Step 5
Keep the compass setting. Place the needle of the compass on point B, and draw an arc that intersects the circle. Mark that intersection (but don't label it).
Step 6
Keep the compass setting. Place the needle of the compass on that new unlabeled point, and draw an arc that intersects the circle. Label the intersection point with the circle as point C.
Step 7
Use a straightedge to draw segments AB¯¯¯¯¯¯¯¯, BC¯¯¯¯¯¯¯¯, and CA¯¯¯¯¯¯¯¯.
Step 8
You should now have an equilateral triangle, △ABC.
Do not erase any of the marks that you made to create the triangle. Your teacher will be looking for them to see if you completed the steps correctly.
Check your work by using a protractor to verify that m∠A=m∠B=m∠C=60∘.
Check your work by using a ruler to verify that AB=BC=CA.
1 answer
1 answer