Geometric Constructions | ClipArt ETC

This mathematics ClipArt gallery offers 213 illustrations of common geometric constructions. Geometric constructions are made with only the use of a compass and a straight edge. In addition to the constructions of different types of polygons, images include those used to show how to bisect a line, angle, and arc.

Illustration of the construction used to create an isosceles triangle, given the bases and the sum of the altitude and a side.

Construction Of An Isosceles Triangle

Illustration of the construction used to create an isosceles triangle, given the bases and the sum of…

An illustration showing the construction used to divide a line AB into two equal parts; and to erect a perpendicular through the middle. "With the end A and B as centers, draw the dotted circle arcs with a radius greater than half the line. Through the crossings of the arcs draw the perpendicular CD, which divides the line into two equal parts."

Construction Of A Line Divided In Equal Parts

An illustration showing the construction used to divide a line AB into two equal parts; and to erect…

Illustration used to show how to find a straight line of the same length as a given arc of a circle.

Construction Of Line Equal To Arc

Illustration used to show how to find a straight line of the same length as a given arc of a circle.

"A regular township, according to United States surveys, is 6 miles square and is divided into 36 equal parts or sections, each section containing 640 acres and measuring one mile square...How many acres or land in 4.75 sections? How many more acres in 7.5 sections than there are in 3 sections? How many acres of land in .5 section?, 2.5 sections?, 5 sections? How many more acres in 3.5 sections than in 2 sections?" -Foster, 1921

Land Measurement

"A regular township, according to United States surveys, is 6 miles square and is divided into 36 equal…

An illustration showing how to construct a regular octagon from a square by cutting off the corners of the square. "With the corners as centers, draw circle arcs through the center of the square to the side, which determine the cut-off."

Construction Of An Octagon From a Square

An illustration showing how to construct a regular octagon from a square by cutting off the corners…

Illustration used to show how to inscribe a regular octagon in a given circle.

Construction Of Octagon Inscribed In Circle

Illustration used to show how to inscribe a regular octagon in a given circle.

An illustration showing how to construct an octagon on a given line. "Prolong AB to C. With B as center and AB as radius, draw the circle AFDEC; from B, draw BI at right angles to AB; divide the angles ABC and DBC each into two equal parts; then BD is one side of the octagon. With A and E as centers, draw the arcs HKE and AKI, which determine the points H and I, and thus complete the octagon as shown in the illustration."

Construction Of An Octagon

An illustration showing how to construct an octagon on a given line. "Prolong AB to C. With B as center…

A problem exercise creating a stretched out or developed image of the octagonal light shade by using the hexagonal pyramid development method.

Development Exercise of Octagonal Light Shade

A problem exercise creating a stretched out or developed image of the octagonal light shade by using…

Problem exercise in drawing a development or a stretchout image of the octagonal roof and finding the true shape of hip rafter by using projections or dividers.

Development Exercise of Octagonal Roof and True Shape of Rafter

Problem exercise in drawing a development or a stretchout image of the octagonal roof and finding the…

Illustration used to show how to draw an egg-shaped oval when given the diameters.

Construction Of Oval

Illustration used to show how to draw an egg-shaped oval when given the diameters.

Illustration used to construct and oval when given the width.

Construction of Oval

Illustration used to construct and oval when given the width.

Illustration used to draw a parabola when given the base and height.

Construction of Parabola Given Base and Height

Illustration used to draw a parabola when given the base and height.

Illustration used to show how to draw a parabola when the axis and longest double ordinate is given.

Construction Of Parabola

Illustration used to show how to draw a parabola when the axis and longest double ordinate is given.

Illustration of the construction used to create a line parallel to a given line.

Construction Of A Parallel Line

Illustration of the construction used to create a line parallel to a given line.

An illustration showing the construction used to erect a parallel line. "With C as a center, draw the dotted arc ED, with E as a center, draw through C the dotted arc F.C. With the radius FC and E as a center, draw the cross arc at D. Join C with the cross at D, which will be the required parallel line.

Construction Of A Parallel

An illustration showing the construction used to erect a parallel line. "With C as a center, draw the…

Illustration used to show how to draw a parallelogram when given the sides and one of the angles.

Construction Of Parallelogram

Illustration used to show how to draw a parallelogram when given the sides and one of the angles.

An illustration showing the construction used to erect a parallelogram given two sides and an angle. "Draw the base line DE, and make the angle FDE = C; lines DE = B and DF = A; complete the parallelogram by cross arcs at G, and the problem is thus solved."

Construction Of A Parallelogram

An illustration showing the construction used to erect a parallelogram given two sides and an angle.…

Parallelogram Used to Construct Equivalent Square

Illustration of a how to construct a square equivalent to a given parallelogram.

An illustration showing how to construct a pentagon inscribed in a circle. "Draw the diameter AB, and from the center C erect the perpendicular CD. Bisect the radius AC at E; with E as center, and DE as radius, draw the arc DE, and the straight line DF is the length of the side of the pentagon."

Construction Of A Pentagon Inscribed In A Circle

An illustration showing how to construct a pentagon inscribed in a circle. "Draw the diameter AB, and…

Illustration used to show how to inscribe a regular pentagon in a given circle.

Construction Of Pentagon Inscribed In Circle

Illustration used to show how to inscribe a regular pentagon in a given circle.

An illustration showing how to construct a pentagon on a given line. "From B erect BC perpendicular to and half the length of AB; join A and C prolonged to D; with C as center and CB as radius, draw the arc BD; then the chord BB is the radius of the circle circumscribing the pentagon. With A and B as centers, and BD as radius, draw the cross O in the center."

Construction Of A Pentagon On A Line

An illustration showing how to construct a pentagon on a given line. "From B erect BC perpendicular…

An illustration showing how to construct a pentagon on a given line without resort to its center. "From B erect Bo perpendicular to and equal to AB; with C as center and Co as radius, draw the arc Do, then AD is the diagonal of the pentagon. With AD as radius and A as center, draw the arc DE; and with E as center and AB as radius, finish the cross E, and thus complete the pentagon."

Construction Of A Pentagon On A Line

An illustration showing how to construct a pentagon on a given line without resort to its center. "From…

Pentagon Constructed to be Similar to Given Pentagons

Illustration of a how to construct a pentagon similar to two given pentagons.

Illustration used to construct a regular pentagon on a given line.

Construction of Regular Pentagon

Illustration used to construct a regular pentagon on a given line.

"An involute is a curve generated by unwrapping an inflexible chord from around a polygon. Thus the involute of any polygon may be drawn by extending its sides, and with the corners of the polygon as successive centers drawing the tangent arcs." —French, 1911

Involute of Pentagon

"An involute is a curve generated by unwrapping an inflexible chord from around a polygon. Thus the…

Illustration of the construction used to make a perpendicular bisector of a straight line.

Construction Of A Perpendicular Bisector Of A Straight Line

Illustration of the construction used to make a perpendicular bisector of a straight line.

Illustration of the construction used to create a perpendicular to a straight line at a given point.

Construction Of A Perpendicular To A Straight Line

Illustration of the construction used to create a perpendicular to a straight line at a given point.

Illustration of the construction used to create a perpendicular to a straight line from a given point not on the line.

Construction Of A Perpendicular To A Straight Line

Illustration of the construction used to create a perpendicular to a straight line from a given point…

An illustration showing the construction used to erect a perpendicular. "With C as a center, draw the dotted circle arcs at A and B equal distances from C. With A and B as centers, draw the dotted circle arcs at D. From the crossing D draw the required perpendicular DC."

Construction Of A Perpendicular

An illustration showing the construction used to erect a perpendicular. "With C as a center, draw the…

An illustration showing the construction used to erect a perpendicular from a point to a line. "With C as a center, draw the dotted circle arc so that it cuts the line at A and B. With A and B as centers, draw the dotted cross arcs at D with equal radii. Draw the required perpendicular through C and crossing D."

Construction Of A Perpendicular

An illustration showing the construction used to erect a perpendicular from a point to a line. "With…

An illustration showing the construction used to erect a perpendicular at the end of a line. "With the point D as a center at a distance from the line, and with AD as radius, draw the dotted circle arc so that it cuts the line at E through E and D, draw the diameter EC: then join C and A, which will be the required perpendicular."

Construction Of A Perpendicular

An illustration showing the construction used to erect a perpendicular at the end of a line. "With the…

Illustration used to show how to inscribe any regular polygon in a given circle.

Construction Of Polygon Inscribed In Circle

Illustration used to show how to inscribe any regular polygon in a given circle.

Transfer Polygon

"ABCD to a new base A'B'. With radii AC and BC describe intersection arcs from centers A'B', locating…

An exercise developed to draw a rolled out or development of the pentagon prism in a 4" by 5" surface.

Pentagon Development Prism Exercise

An exercise developed to draw a rolled out or development of the pentagon prism in a 4" by 5" surface.

An exercise in drawing a pentagonal prism development or rolled out image in a 4" by 5" area.

Pentagonal Prism Development Exercise

An exercise in drawing a pentagonal prism development or rolled out image in a 4" by 5" area.

An illustration to exercise a stretched out, or development, image of the triangular prism using 4" by 5 " surface.

Triangular Prism Development Exercise

An illustration to exercise a stretched out, or development, image of the triangular prism using 4"…

An illustration to draw triangle prism's development, or stretched out surfaces, in a 4" by 5" surface.

Triangle Prism Exercise

An illustration to draw triangle prism's development, or stretched out surfaces, in a 4" by 5" surface.

An illustration of Axonometric Projection, or object related by plane of projection, of a cube. The cube is drawn by having the cube resting on one side, then projecting each horizontal and vertical lines from A.

Axonometric Projection of a Cube

An illustration of Axonometric Projection, or object related by plane of projection, of a cube. The…

"The axes or edges, CG and CD, are foreshortened a like amount, while CB is foreshortened twice that of the other two. The angles of these axes being known and the reduced scale due to the foreshortening being given, the making of the projection is very simple." —Anthony, 1904

Axonometric Projection of a Rectangular Cube

"The axes or edges, CG and CD, are foreshortened a like amount, while CB is foreshortened twice that…

A rectangular cube drawn by using oblique projection. The original cube was projected parallel at a certain angle. The cube was drawn by drawing the front square in the front, then projecting it in an angle while connecting the edges.

Oblique Projection of a Rectangular Cube

A rectangular cube drawn by using oblique projection. The original cube was projected parallel at a…

An illustration showing the construction used to divide the line AB in the same proportion of parts as AC. "Join C and B, and through the given divisions 1, 2, and 3 draw lines parallel with CB, which solves the problem."

Divide A Line Proportionately

An illustration showing the construction used to divide the line AB in the same proportion of parts…

A sample exercise problem in completing the top part of the hexagonal pyramid and to create a development, or stretched out, of the image by creating edges at equal lengths, and revolving the sides.

Development Exercise of Hexagonal Pyramid

A sample exercise problem in completing the top part of the hexagonal pyramid and to create a development,…

A sample exercise problem to complete the top part and create a stretched out image of the oblique hexagonal pyramid. The stretched out image is created by drawing an arc with the perimeter of the base stepped off to create an intersection point.

Development Exercise of Oblique Hexagonal Pyramid

A sample exercise problem to complete the top part and create a stretched out image of the oblique hexagonal…

A pentagonal pyramid problem exercise to complete the top view of the image, and development, or rolled out image, of the pyramid.

Development Exercise of Pentagonal Pyramid

A pentagonal pyramid problem exercise to complete the top view of the image, and development, or rolled…

The problem exercise in completing the top view and creating the development, or rolled out, image of the pentagonal pyramid.

Development Exercise of Pentagonal Pyramid

The problem exercise in completing the top view and creating the development, or rolled out, image of…

Construction of Radii of a Circle

Illustration used to draw lines which are radii of a circle where the center is inaccessible.

"Let OA and OB be the asymptotes and P a point on the curve. Draw PC and PD. Mark any points on Pc; through these points draw ordinates parallel to OA and through the same points lines to O. At the intersection of these lines with PD draw abscissæ with the ordinates give points on the curve." —French, 1911

Drawing Rectangular Hyperbola

"Let OA and OB be the asymptotes and P a point on the curve. Draw PC and PD. Mark any points on Pc;…

"In ordinary work the usual way of rectifying an arc is to step around it with the dividers, in spaces small enough as practically to coincide with the arc, and to step off the same number on the right line." —French, 1911

Rectifying Arc Using Dividers

"In ordinary work the usual way of rectifying an arc is to step around it with the dividers, in spaces…

"Draw the diagonals of the square. With the corners of the square as centers and radius of half the diagonal draw arcs intersecting the sides of the square and connect these points." —French, 1911

Inscribe Regular Octagon in Given Square

"Draw the diagonals of the square. With the corners of the square as centers and radius of half the…

An illustration showing how to construct a regular polygon on a given line without resort to its center. "Extend AB to C and, with B as center, draw the half circle ADB. Divide the half circle into as many parts as the number of sides in the polygon, and complete the construction as shown on the illustration."

Construction Of A Regular Polygon On A Line

An illustration showing how to construct a regular polygon on a given line without resort to its center.…

Illustration used to show how to draw a regular polygon when given a side of the polygon.

Construction Of Regular Polygon

Illustration used to show how to draw a regular polygon when given a side of the polygon.

Make a perpendicular lines at point B and C, and join by a straight line. Create a desired curve by referencing the lines as a center and tangent.

Draw Reverse or Ogee Curve

Make a perpendicular lines at point B and C, and join by a straight line. Create a desired curve by…

"A series of planes as S—S are passed perpendicular to the axis of revolution, cutting out the circles shown on the end view. The points at which these circles cut the 'flat' are projected back as points on the curve." —French, 1911

Intersection of Surface of Revolution and Plane

"A series of planes as S—S are passed perpendicular to the axis of revolution, cutting out the…

"DE being chosen as an isometric line or axis, a second axis, YY, is drawn isometrically perpendicular to it. Points C and F lie on this axis, and their position is readily determined, since measurements may be made on this line. As line AB, drawn through C, is an isometric line, points A and B may be located at their proper distances to the right and left of the axis YY." —Anthony, 1904

Pentagon Elevation and Projection Scaling

"DE being chosen as an isometric line or axis, a second axis, YY, is drawn isometrically perpendicular…

An illustration showing how to construct a screw helix.

Construction Of A Screw Helix

An illustration showing how to construct a screw helix.

An illustration showing how to construct a square circumscribed about a circle. "Draw the diameters AB and CD at right angles to one another; with the radius of the circle, and A, B, C, and D as centers, draw the four dotted half circles which cross one another in the corners of the square, and thus complete the problem."

Construction Of A Square Circumscribed About A Circle

An illustration showing how to construct a square circumscribed about a circle. "Draw the diameters…

An illustration showing how to construct a square upon a given line. "With AB as radius and A and B as centers, draw the circle arcs AED and BEC. Divide the arc BE in two equal parts at F, and with EF as radius and E as center, draw the circle CFD. Join A and CB and D, C and D, which completes the required square."

Square Constructed Upon A Given Line

An illustration showing how to construct a square upon a given line. "With AB as radius and A and B…

An illustration showing how to construct a square inscribed in a circle. "Draw the diameter AB, and through the center erect the perpendicular CD, and complete the square as shown in the illustration."

Construction Of A Square Inscribed In A Circle

An illustration showing how to construct a square inscribed in a circle. "Draw the diameter AB, and…

Illustration used to show how to inscribe a square in a given circle.

Construction Of Square Inscribed In Circle

Illustration used to show how to inscribe a square in a given circle.

Illustration used to construct a square on a given line.

Construction of Square on Given Line

Illustration used to construct a square on a given line.

1
2
3
4