Show A 90 Degree Angle

Constructing a 90° bending

On this page nosotros show how to construct (describe) a 90 degree angle with compass and straightedge or ruler. There are various ways to do this, but in this construction we apply a property of Thales Theorem. We create a circumvolve where the vertex of the desired correct angle is a point on a circumvolve. Thales Theorem says that whatever diameter of a circumvolve subtends a right angle to whatsoever point on the circumvolve.

Printable pace-by-step instructions

The in a higher place animation is available every bit a printable pace-past-step instruction sheet, which can be used for making handouts or when a computer is non available.

Explanation of method

This is actually the same structure equally Amalgam a perpendicular at the endpoint of a ray. Some other way to do it 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 apex of the desired right angle is a bespeak on a circle.

	Argument	Reason
1	The line segment AB is a bore of the circle middle D	AB is a directly line through the center.
2	Bending ACB has a measure of 90°.	The diameter of a circumvolve ever subtends an angle of 90° to any point (C) on the circumvolve. See Thales theorem.

- Q.E.D

Try it yourself

Click here for a printable worksheet containing two bug to try. When you get to the page, use the browser print command to print 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
Copy a line segment
Sum of n line segments
Deviation of two line segments
Perpendicular bisector of a line segment
Perpendicular at a betoken on a line
Perpendicular from a line through a point
Perpendicular from endpoint of a ray
Divide a segment into northward equal parts
Parallel line through a point (angle copy)
Parallel line through a point (rhomb)
Parallel line through a point (translation)

Angles

Bisecting an angle
Copy an angle
Construct a xxx° bending
Construct a 45° angle
Construct a sixty° angle
Construct a 90° bending (right angle)
Sum of n angles
Deviation of two 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
thirty-60-xc triangle, given the hypotenuse
Triangle, given iii sides (sss)
Triangle, given i side and side by side angles (asa)
Triangle, given two angles and non-included side (aas)
Triangle, given ii sides and included angle (sas)
Triangle medians
Triangle midsegment
Triangle altitude
Triangle altitude (exterior case)

Correct triangles

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

Triangle Centers

Triangle incenter
Triangle circumcenter
Triangle orthocenter
Triangle centroid

Circles, Arcs and Ellipses

Finding the center of a circumvolve
Circle given three points
Tangent at a signal 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
Square inscribed in a circumvolve
Hexagon given one side
Hexagon inscribed in a given circle
Pentagon inscribed in a given circle

Non-Euclidean constructions

Construct an ellipse with cord and pins
Observe the middle of a circumvolve with any right-angled object