Constructing a 60° angle

This page shows how to construct (draw) a 60 caste angle with compass and straightedge or ruler. This construction works past creating an equilateral triangle. Remember that an equilateral triangle has all three interior angles 60°. Nosotros use one of those angles to get the desired lx degree result. Come across the proof below for more than details.

Printable step-by-step instructions

The to a higher place animation is available as a printable step-by-step didactics sheet, which can be used for making handouts or when a computer is not available.

Proof

This structure works by creating an equilateral triangle. Recollect that an equilateral triangle has all three interior angles 60°. The image below is the final drawing to a higher place with the reddish items added.

	Statement	Reason
1	Line segments AB, Lead, PA are congruent	All drawn with the same compass width.
two	Triangle APB is an equilateral triangle	Equilateral triangles are those with all three sides the same length.
3	Angle APB has a measure of 60°	All 3 interior angles of an equilateral triangle have a measure of 60°. Run across Equilateral triangle definition

- Q.E.D

Try it yourself

Click here for a printable worksheet containing two sixty° angle exercises. When you become to the page, use the browser print control to print as many as you wish. The printed output is non copyright.

Other constructions pages on this site

Listing of printable constructions worksheets

Lines

Introduction to constructions
Copy a line segment
Sum of n 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 bespeak
Perpendicular from endpoint of a ray
Divide a segment into n equal parts
Parallel line through a point (angle copy)
Parallel line through a indicate (rhomb)
Parallel line through a point (translation)

Angles

Bisecting an angle
Copy an angle
Construct a 30° angle
Construct a 45° bending
Construct a sixty° angle
Construct a 90° bending (right bending)
Sum of n angles
Difference of ii angles
Supplementary angle
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 altitude
Isosceles triangle, given leg and apex angle
Equilateral triangle
thirty-60-ninety triangle, given the hypotenuse
Triangle, given 3 sides (sss)
Triangle, given ane side and adjacent angles (asa)
Triangle, given two angles and non-included side (aas)
Triangle, given two sides and included angle (sas)
Triangle medians
Triangle midsegment
Triangle distance
Triangle altitude (outside instance)

Correct triangles

Right Triangle, given one leg and hypotenuse (HL)
Right Triangle, given both legs (LL)
Right Triangle, given hypotenuse and 1 bending (HA)
Right Triangle, given one leg and one angle (LA)

Triangle Centers

Triangle incenter
Triangle circumcenter
Triangle orthocenter
Triangle centroid

Circles, Arcs and Ellipses

Finding the center of a circle
Circumvolve given 3 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 one side
Foursquare inscribed in a circle
Hexagon given one side
Hexagon inscribed in a given circle
Pentagon inscribed in a given circumvolve

Non-Euclidean constructions

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

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How to Draw a 60 Degree Angle Without a Protractor TUTORIAL

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How to Draw a 60 Degree Angle Without a Protractor TUTORIAL. There are any How to Draw a 60 Degree Angle Without a Protractor TUTORIAL in here.