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The following statements are true in Euclidean geometry. I. The sum of the interior angles of a triangle is always 180 and deg. II. It is possible to construct an equilateral triangle. III. At most a?

In Euclidean geometry, the statements are true: I. The sum of the interior angles of a triangle is always 180 degrees; II. It is indeed possible to construct an equilateral triangle, as it can be done with a compass and straightedge; III. At most, a triangle has three sides, as defined by its geometric properties.


What tools or construction is needed to construct an equilateral triangle?

To construct an equilateral triangle, you need a straightedge (ruler without markings) and a compass. First, draw a straight line segment of the desired length for one side of the triangle. Then, use the compass to draw arcs from each endpoint of the segment, with the radius set to the length of the segment, intersecting the arcs to find the third vertex. Finally, connect the vertices to complete the equilateral triangle.


To construct a angle you first construct an equilateral triangle?

Yes


Can you construct an equiangular triangle that is not equilateral?

No, you can't.


What triangle do you need to construct in order to trisect a right angle?

An equilateral triangle.


Is it possible to make an obtuse equilateral triangle?

No. It is not possible to make a equilateral triangle that is obtuse.


To trisect an angle you first construct an equilateral triangle?

Right


You can draw a regular hexagon using only a straightedge and compass by first building an equilateral triangle?

trueee


You can draw a regular hexagon using only a straightedge and compass by the first building an equilateral triangle?

True...


An equilateral triangle with sides measuring 8cm 9cm and 10 cm?

This is not an equilateral triangle.


Is it possible to draw an equilateral acute triangle?

Yes, because an equilateral triangle is always acute.


Is it possible to sketch a right equilateral triangle?

No. In an equilateral triangle, all three angles are the same. Since they are not ninety degrees, you can't have a right triangle that is also an equilateral triangle.