Any acute triangle can form a parallelogram when fitted to another rotated by 180°.
So can it tessellate the plane?
How do you know?
So can it tessellate the plane?
Acute means all angles are below 90.
By the way, which level of math are you doing?
Tessellation, also known as tiling, is the process of covering a plane (2D surface) with repeated shapes without any gaps or overlaps. The shapes used in tessellation are called tiles, and they are typically regular polygons (shapes with equal angles and equal side lengths).
A regular acute triangle has three equal angles of less than 90 degrees each. However, to tessellate the plane, the angles of a shape need to evenly divide 360 degrees (the complete angle around a point) without any remainder. In a regular acute triangle, each angle is less than 90 degrees, so three of them cannot add up to 360 degrees. Therefore, a regular acute triangle cannot tessellate the plane.
On the other hand, a non-regular acute triangle has angles that are not equal. In this case, we need to check whether the angles can add up to 360 degrees. If the angles of the non-regular acute triangle add up to exactly 360 degrees, then it can tessellate the plane.
To determine if the angles add up to 360 degrees, you can follow these steps:
1. Measure the angles of the non-regular acute triangle using a protractor.
2. Add the measurements of the three angles together.
3. If the sum equals 360 degrees, then the non-regular acute triangle can tessellate the plane.
By following these steps, you can verify if a non-regular acute triangle tessellates the plane or not.