Construction Equilateral Triangle

Which of the following constructions is illustrated?

• An angle is congruent to a given angle

• The bisector of a given angle

• equilateral triangle

• The perpendicular bisector of a given segment.

A triangle with all sides in equal length is 

• an obtuse triangle. 

• a right triangle.

• an isosceles triangle.

• an equilateral triangle.

To construct an equilateral triangle, all you need is a compass and a straightedge.

• True

• False

Which of the following steps is the first in constructing an equilateral triangle using a compass and straightedge?

• Draw a line segment of any length.

• Draw a circle with a given radius.

• Draw two intersecting circles with the same radius.

• Draw a perpendicular bisector of a line segment.

A "Yield" sign is an equiangular triangle. What are the lengths of the sides?

Mathematical Equivalence

OFF

After drawing a line segment, what is the next step in constructing an equilateral triangle using a compass and straightedge?

• Draw a perpendicular bisector of the line segment.

• Draw a circle with the center at one endpoint of the line segment and radius equal to the length of the line segment.

• Draw a circle with the center at the midpoint of the line segment.

• Draw a parallel line through one endpoint of the line segment.

What is the purpose of drawing two circles with the same radius from each endpoint of the line segment in the construction of an equilateral triangle?

• To find the midpoint of the line segment.

• To find the intersection point which will be the third vertex of the equilateral triangle.

• To create a perpendicular bisector.

• To create a parallel line.

Which geometric tool is essential for ensuring that all sides of the triangle are equal when constructing an equilateral triangle?

• Protractor

• Compass

• Ruler

• Set square

When constructing an equilateral triangle inscribed in a circle, what is the first step?

• Draw a radius of the circle.

• Draw a diameter of the circle.

• Draw a circle with a given radius.

• Draw a tangent to the circle.

What is the next step after marking three equal arcs on the circumference of the circle when constructing an equilateral triangle inscribed in a circle?

• Connect the center of the circle to each arc.

• Connect the points where the arcs intersect the circumference.

• Draw a tangent line at each arc.

• Draw a perpendicular bisector of each arc.