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.

A line which is divided into equal parts, shown by construction and square.

Construction of Dividing Lines

A line which is divided into equal parts, shown by construction and square.

Illustration of the construction used to create an equal angle given a point in a given straight line and a given angle.

Construction of an Equal Angle Given a Point and a Straight Line

Illustration of the construction used to create an equal angle given a point in a given straight line…

Illustration of the construction used to escribe circles with centres (centers) called ex-centres of the triangles. The intersections of the bisectors of the exterior angles of a triangle are the centers of three circles, each of which will touch one side of the triangle, and the two other circles.

Construction of Escribed Circles With Ex-centres

Illustration of the construction used to escribe circles with centres (centers) called ex-centres of…

Illustration of the construction used to find the third angle of a triangle when two of the angles are given.

Construction to Find the Third Angle of a Triangle When Given Two Angles

Illustration of the construction used to find the third angle of a triangle when two of the angles are…

Illustration used to construct a circle that shall pass through a given point and cut chords of a given length from two parallels.

Construction of a Circle Through a Given Point that Cuts Chords of Given Lengths From Parallels

Illustration used to construct a circle that shall pass through a given point and cut chords of a given…

Construction to Inscribe a Circle in a Triangle

Illustration of the construction used to inscribe a circle in a given triangle.

Construction of a Parallelogram When Given Two Sides and Included Angle

Illustration of the construction used to make a parallelogram when given two sides and the included…

Illustration to let fall a perpendicular upon a given line from a given external point.

Construction of Perpendicular Upon a Given Line From an External Point

Illustration to let fall a perpendicular upon a given line from a given external point.

Illustration of the construction of a perpendicular to a line when given a point O on the straight line.

Construction of Perpendicular From a Given Point on a Straight Line

Illustration of the construction of a perpendicular to a line when given a point O on the straight line.

Illustration of the construction of a perpendicular to a line when given a point B on the straight line.

Construction of Perpendicular From a Given Point on a Straight Line

Illustration of the construction of a perpendicular to a line when given a point B on the straight line.

Illustration of the construction used upon a given straight line, to describe a segment of a circle in which a given angle may be inscribed.

Construction to Describe a Segment of a Circle in Which an Angle Can Be Inscribed

Illustration of the construction used upon a given straight line, to describe a segment of a circle…

Construction of a Straight Line Divided Into Equal Parts

Illustration of the construction used to divide a straight line into a given number of equal parts.

Illustration of the construction used to create straight line parallel to a given straight line through a given external point.

Construction of a Straight Line Parallel to a Given Straight Line

Illustration of the construction used to create straight line parallel to a given straight line through…

Construction of Tangent Line Through a Given Point to a Given Circle

Illustration of the construction used to draw a tangent to a given circle through a given point.

Illustration of the construction used to make a triangle when given two sides and the angle opposite one of them. This is for case 1 of the ambiguous case, when a is less than b.

Construction of a Triangle When Given Two Sides and the Angle Opposite (Ambiguous Case)

Illustration of the construction used to make a triangle when given two sides and the angle opposite…

Illustration of the construction used to make a triangle when given two sides and the angle opposite one of them. This is for case 2 of the ambiguous case, when a is equal to b.

Construction of a Triangle When Given Two Sides and the Angle Opposite (Ambiguous Case)

Illustration of the construction used to make a triangle when given two sides and the angle opposite…

Illustration of the construction used to make a triangle when given two sides and the angle opposite one of them. This is for case 2 of the ambiguous case, when a is equal to b.

Construction of a Triangle When Given Two Sides and the Angle Opposite (Ambiguous Case)

Illustration of the construction used to make a triangle when given two sides and the angle opposite…

Construction of a Triangle Given Perimeter, Angle, Altitude

Illustration used to construct a triangle , given the perimeter, one angle, and the altitude from the…

Construction of a Triangle When Given a Side and Two Angles

Illustration of the construction used to make a triangle when given a side and two angles.

Construction of a Triangle When Given Three Sides

Illustration of the construction used to make a triangle when given three sides.

Construction of a Triangle When Given Two Sides and Included Angle

Illustration of the construction used to make a triangle when given two sides and the included angle.

"Any noncircular curve may be approximated by tangent circle arcs, selecting a center by trial, drawing as much of an arc as will practically coincide with the curve, then changing the center and radius for the next portion, remembering always that if arcs are to be tangent, their centers must lie on the common normal at the point of tangency." —French 1911

Curve Inked with Circle Arcs

"Any noncircular curve may be approximated by tangent circle arcs, selecting a center by trial, drawing…

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the cone and parallel to the cylinder; or by cutting circles from the right cone perpendicular to the axes.

Intersection of Cylinder and Cone

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the…

Cycloid

"A cycloid is the curve generated by the motion of a point on the circumference of a circle rolled along…

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the cone and parallel to the cylinder; or by cutting circles from the right cone perpendicular to the axes.

Intersection of Cylinder and Cone

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the…

An exercise problem in creating a development or rolled out surface of a cylinder in a 4" by 5" drawing area.

Development Exercise of Cylinder

An exercise problem in creating a development or rolled out surface of a cylinder in a 4" by 5" drawing…

An illustration showing how to construct a cyma, or two circle arcs that will tangent themselves, and two parallel lines at given points A and B. "Join A and B; divide AB into four equal parts and erect perpendiculars. Draw Am at right angles from A, and Bn at right angles from B; then m and n are the centers of the circle arcs of the required cyma."

Construction Of A Cyma

An illustration showing how to construct a cyma, or two circle arcs that will tangent themselves, and…

Using C as a center, draw two circles with different diameters. The intersection of the diameter lines will determine the points on the curve.

Determining Points on Ellipse Using Circles

Using C as a center, draw two circles with different diameters. The intersection of the diameter lines…

A development, or rolled out, cone where the point A is the meeting point for the sides. The development is drawn by drawing the arc by using a compass.

Development of Cone

A development, or rolled out, cone where the point A is the meeting point for the sides. The development…

A rolled out, or development, of the cylinder. The development is created by drawing the top curve with the dashed line where the folds are.

Development of Cylinder

A rolled out, or development, of the cylinder. The development is created by drawing the top curve with…

The development, or unfolded prism, of the rectangular pyramid. The sides of the prism is joined at point E for reference, and the shape of the sides are by using the reference point.

Development of Rectangle Pyramid

The development, or unfolded prism, of the rectangular pyramid. The sides of the prism is joined at…

A development, or rolled out, triangle pyramid. The image is created by making an arc at the bottom of each triangles to guide the straight lines. The triangle ABC is the base of the pyramid. When folded, the pyramid will form from the image.

Development of Triangle Pyramid

A development, or rolled out, triangle pyramid. The image is created by making an arc at the bottom…

A development, or rolled out image, of two cylinders intersecting each other. The large rectangular diagram is the main cylindrical body with a circle inside it for the other cylinder. The smaller development is the intersected cylinder. This is commonly used to illustrate pipes.

Development of Two Intersecting Cylinder

A development, or rolled out image, of two cylinders intersecting each other. The large rectangular…

Illustration used to show how to divide a line into any number of equal parts by construction.

Construction Used to Divide a Line Into Equal Parts

Illustration used to show how to divide a line into any number of equal parts by construction.

Illustration used to show how to divide a given straight line into required number of equal parts.

Construction Of Dividing A Line

Illustration used to show how to divide a given straight line into required number of equal parts.

Illustration used to show how to divide a given straight line into required number of equal parts.

Construction Of Dividing A Line

Illustration used to show how to divide a given straight line into required number of equal parts.

A development or rolled out image exercise problem of the dome and finding the true shape of the hip, or edge, of the dome by using projections or with dividers.

Development Exercise of Dome and True Shape of Hip

A development or rolled out image exercise problem of the dome and finding the true shape of the hip,…

"Draw three-inch square and one-inch square. From the corners of inner square draw lines to outer square at 15 degrees and 75 degrees, with the two triangles in combination. Mark points with spacers 3/16" inside of each line of this outside cross, and complete figure with triangles in combination." —French, 1911

Drawing Maltese Cross using T-square, Spacers, and Triangles

"Draw three-inch square and one-inch square. From the corners of inner square draw lines to outer square…

An illustration showing how to construct an ellipse parallel to two parallel lines A and B. "Draw a semicircle on AB, draw ordinates in the circle at right angle to AB, the corresponding and equal ordinates for the ellipse to be drawn parallel to the lines, and thus the elliptic curve is obtained as shown by the figure."

Construction Of An Ellipse Tangent To Two Parallel Lines

An illustration showing how to construct an ellipse parallel to two parallel lines A and B. "Draw a…

Illustration used to show how to draw an ellipse when given the diameters.

Construction Of Ellipse

Illustration used to show how to draw an ellipse when given the diameters.

Illustration used to show how to draw an ellipse by circular arcs.

Construction Of Ellipse

Illustration used to show how to draw an ellipse by circular arcs.

Epicycloid is generated by a circle rolled outside of another circle, whereas a hypocycloid is circle rolled inside another circle.

Epicycloid and Hypocycloid

Epicycloid is generated by a circle rolled outside of another circle, whereas a hypocycloid is circle…

Construction Of An Equal Angle

Illustration used to show how to construct an angle equal to a given angle when given a vertex and a…

An illustration showing the construction used to erect an equal angle. "With D as a center, draw the dotted arc CE: and with the same radius and B as a center, draw the arc GF; then make GF equal to CE; then join BF, which will form the required angle, FBG=CDE."

Construction Of An Equal Angle

An illustration showing the construction used to erect an equal angle. "With D as a center, draw the…

Illustration used to show how to divide a given straight line into any number of equal parts.

Line Divided Into Equal Parts

Illustration used to show how to divide a given straight line into any number of equal parts.

An illustration showing how to construct an equilateral triangle inscribed in a circle. "With the radius of the circle and center C draw the arc DFE; with the same radius, and D and E as centers, set off the points A and B. Join A and B, B and C, C and A, which will be the required triangle."

Construction Of An Equilateral Triangle Inscribed In A Circle

An illustration showing how to construct an equilateral triangle inscribed in a circle. "With the radius…

Illustration used to show how to construct an equilateral triangle, with a given line as a side.

Construction Of Equilateral Triangle

Illustration used to show how to construct an equilateral triangle, with a given line as a side.

Illustration used to show how to draw an equilateral triangle when given one side.

Construction Of Equilateral Triangle

Illustration used to show how to draw an equilateral triangle when given one side.

Illustration used to show how to draw an equilateral triangle when given the altitude.

Construction Of Equilateral Triangle

Illustration used to show how to draw an equilateral triangle when given the altitude.

Illustration used to show how "to construct a common external tangent to two given circles."

Construction of an External Tangent to 2 Circles

Illustration used to show how "to construct a common external tangent to two given circles."

Illustration used to show how to construct two common external tangents to two given circles.

Construction of an 2 External Tangents to 2 Circles

Illustration used to show how to construct two common external tangents to two given circles.

Geometrical perspective drawing.

Geometrical Perspective

Geometrical perspective drawing.

Illustration used to show how to draw a helix when the pitch and the diameter are given.

Construction Of Helix

Illustration used to show how to draw a helix when the pitch and the diameter are given.

An illustration showing how to construct a heptagon, or septagon. "The appotem a in a hexagon is the length of the side of the heptagon. Set off AB equal to the radius of the circle; draw a from the center C at right angles to AB; then a is the required side of the heptagon."

Construction Of A Heptagon

An illustration showing how to construct a heptagon, or septagon. "The appotem a in a hexagon is the…

An illustration showing how to construct a hexagon in a given circle. "The radius of the circle is equal to the side of the hexagon."

Construction Of A Hexagon In A Circle

An illustration showing how to construct a hexagon in a given circle. "The radius of the circle is equal…

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

Construction Of Hexagon Inscribed In Circle

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

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

Construction of Regular Hexagon

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

Illustration of a how to construct a triangle equivalent to a given hexagon/polygon.

Hexagon Used to Construct Equivalent Triangle

Illustration of a how to construct a triangle equivalent to a given hexagon/polygon.

"Through the center of the space draw the three construction lines, AB vertical, DE and FG at 30 degrees. Measure CA and CB 1 1/2" long. Draw AE, AF, DB and BG at 30 degrees. Complete hexagon by drawing DF and GE vertical. Set spacers to 3/32". Step off 3/32" on each side of the center lines, and 3/16" from each side of hexagon. Complete figure as shown with triangle against T-square." —French, 1911

Drawing Hexagonal Figure

"Through the center of the space draw the three construction lines, AB vertical, DE and FG at 30 degrees.…

Construction of a regular hexagonal pyramid.

Construction of Hexagonal Pyramid

Construction of a regular hexagonal pyramid.

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