How To Draw Equilateral Triangle

Constructing an Equilateral Triangle

This folio shows how to construct an equilateral triangle with compass and straightedge or ruler. An equilateral triangle is one with all iii sides the same length. It begins with a given line segment which is the length of each side of the desired equilateral triangle.

It works because the compass width is not inverse between drawing each side, guaranteeing they are all coinciding (same length). It is similar to the 60 caste angle construction, because the interior angles of an equilateral triangle are all sixty degrees.

Printable step-by-step instructions

The above animation is available equally a printable step-by-footstep educational activity sheet, which tin be used for making handouts or when a computer is not bachelor.

Proof

The image below is the final drawing in a higher place.

	Argument	Reason
1	PQ, PR and QR are all coinciding to AB and then all accept the aforementioned length	Compass width set from AB used to draw them all
two	Triangle RPQ is an equilateral triangle with the given side length AB.	All 3 sides congruent. See Equilateral triangle definition.

- Q.East.D

Endeavor it yourself

Click here for a printable worksheet containing 2 bug to try. When you lot get to the page, apply the browser print command to print as many as y'all wish. The printed output is not copyright.

Other constructions pages on this site

List of printable constructions worksheets

Lines

Introduction to constructions
Copy a line segment
Sum of n line segments
Difference of ii line segments
Perpendicular bisector of a line segment
Perpendicular at a point on a line
Perpendicular from a line through a point
Perpendicular from endpoint of a ray
Split up a segment into n equal parts
Parallel line through a point (bending re-create)
Parallel line through a point (rhombus)
Parallel line through a point (translation)

Angles

Bisecting an bending
Copy an angle
Construct a thirty° angle
Construct a 45° angle
Construct a threescore° angle
Construct a 90° angle (right angle)
Sum of n angles
Difference of two angles
Supplementary bending
Complementary angle
Constructing 75° 105° 120° 135° 150° angles and more than

Triangles

Copy a triangle
Isosceles triangle, given base and side
Isosceles triangle, given base and distance
Isosceles triangle, given leg and apex angle
Equilateral triangle
30-lx-90 triangle, given the hypotenuse
Triangle, given 3 sides (sss)
Triangle, given one side and next angles (asa)
Triangle, given 2 angles and not-included side (aas)
Triangle, given two sides and included angle (sas)
Triangle medians
Triangle midsegment
Triangle altitude
Triangle altitude (outside case)

Right triangles

Right Triangle, given one leg and hypotenuse (HL)
Right Triangle, given both legs (LL)
Right Triangle, given hypotenuse and one angle (HA)
Right Triangle, given one leg and i angle (LA)

Triangle Centers

Triangle incenter
Triangle circumcenter
Triangle orthocenter
Triangle centroid

Circles, Arcs and Ellipses

Finding the center of a circumvolve
Circle given iii points
Tangent at a point on the circle
Tangents through an external point
Tangents to two circles (external)
Tangents to two circles (internal)
Incircle of a triangle
Focus points of a given ellipse
Circumcircle of a triangle

Polygons

Square given 1 side
Square inscribed in a circle
Hexagon given i side
Hexagon inscribed in a given circle
Pentagon inscribed in a given circumvolve

Non-Euclidean constructions

Construct an ellipse with string and pins
Find the centre of a circle with any right-angled object