90 Degrees On A Compass

Amalgam a 90° bending

On this page we prove how to construct (depict) a xc degree angle with compass and straightedge or ruler. There are diverse ways to do this, merely in this structure nosotros utilize a property of Thales Theorem. We create a circle where the vertex of the desired right angle is a point on a circle. Thales Theorem says that any bore of a circle subtends a right angle to any point on the circle.

Printable step-past-stride instructions

The above animation is available as a printable step-past-footstep instruction canvas, which can be used for making handouts or when a estimator is non available.

Caption of method

This is really the aforementioned construction as Constructing a perpendicular at the endpoint of a ray. Another way to practice information technology is to

construct a perpendicular at a signal on a line or
construct a perpendicular to a line from an external point

Proof

This construction works by using Thales theorem. It creates a circle where the noon of the desired right bending is a betoken on a circle.

	Argument	Reason
1	The line segment AB is a bore of the circumvolve center D	AB is a directly line through the center.
2	Angle ACB has a mensurate of ninety°.	The diameter of a circle ever subtends an angle of ninety° to any signal (C) on the circumvolve. Meet Thales theorem.

- Q.Due east.D

Endeavour it yourself

Click hither for a printable worksheet containing two problems to try. When you lot go to the page, use the browser print command to impress as many as you wish. The printed output is not copyright.

Other constructions pages on this site

List of printable constructions worksheets

Lines

Introduction to constructions
Re-create 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 a segment into n equal parts
Parallel line through a indicate (angle copy)
Parallel line through a betoken (rhombus)
Parallel line through a point (translation)

Angles

Bisecting an bending
Copy an angle
Construct a xxx° angle
Construct a 45° angle
Construct a 60° angle
Construct a 90° angle (right angle)
Sum of n angles
Difference of ii angles
Supplementary bending
Complementary bending
Constructing 75° 105° 120° 135° 150° angles and more

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
30-lx-90 triangle, given the hypotenuse
Triangle, given iii sides (sss)
Triangle, given one side and adjacent angles (asa)
Triangle, given two angles and non-included side (aas)
Triangle, given two sides and included bending (sas)
Triangle medians
Triangle midsegment
Triangle altitude
Triangle altitude (outside example)

Correct triangles

Right Triangle, given i leg and hypotenuse (HL)
Correct Triangle, given both legs (LL)
Right Triangle, given hypotenuse and one 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 center of a circle
Circumvolve 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 ane side
Foursquare inscribed in a circle
Hexagon given i side
Hexagon inscribed in a given circumvolve
Pentagon inscribed in a given circle

Non-Euclidean constructions

Construct an ellipse with string and pins
Find the eye of a circle with whatever correct-angled object