How To Draw A Equilateral Triangle

Constructing an Equilateral Triangle

This page shows how to construct an equilateral triangle with compass and straightedge or ruler. An equilateral triangle is one with all three 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 non changed betwixt drawing each side, guaranteeing they are all coinciding (same length). It is similar to the threescore degree bending construction, because the interior angles of an equilateral triangle are all 60 degrees.

Printable footstep-by-step instructions

The above blitheness is available equally a printable step-by-step instruction canvas, which tin be used for making handouts or when a calculator is non available.

Proof

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

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

- Q.East.D

Effort it yourself

Click here for a printable worksheet containing 2 issues to try. When you get to the page, use the browser print command to print as many as you lot wish. The printed output is non copyright.

Other constructions pages on this site

List of printable constructions worksheets

Lines

Introduction to constructions
Copy a line segment
Sum of due north line segments
Difference of two 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 a segment into n equal parts
Parallel line through a bespeak (angle copy)
Parallel line through a point (rhombus)
Parallel line through a point (translation)

Angles

Bisecting an bending
Copy an angle
Construct a 30° angle
Construct a 45° bending
Construct a sixty° angle
Construct a 90° bending (correct bending)
Sum of n angles
Difference of two angles
Supplementary angle
Complementary angle
Constructing 75° 105° 120° 135° 150° angles and more

Triangles

Re-create a triangle
Isosceles triangle, given base and side
Isosceles triangle, given base and altitude
Isosceles triangle, given leg and apex bending
Equilateral triangle
30-60-90 triangle, given the hypotenuse
Triangle, given 3 sides (sss)
Triangle, given one side and adjacent angles (asa)
Triangle, given two angles and non-included side (aas)
Triangle, given 2 sides and included angle (sas)
Triangle medians
Triangle midsegment
Triangle altitude
Triangle altitude (exterior case)

Right triangles

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

Triangle Centers

Triangle incenter
Triangle circumcenter
Triangle orthocenter
Triangle centroid

Circles, Arcs and Ellipses

Finding the middle of a circle
Circle given 3 points
Tangent at a point on the circle
Tangents through an external point
Tangents to two circles (external)
Tangents to ii circles (internal)
Incircle of a triangle
Focus points of a given ellipse
Circumcircle of a triangle

Polygons

Square given one side
Square inscribed in a circle
Hexagon given one side
Hexagon inscribed in a given circle
Pentagon inscribed in a given circle

Non-Euclidean constructions

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

Source: https://www.mathopenref.com/constequilateral.html

Posted by: morristhadell.blogspot.com