This mathematics ClipArt gallery offers 38 illustrations that can be used when teaching the concept of proportionality. A proportion is an equation stating that two ratios are equal. Images are of similar figures, including those that can be used in application problems.

"The distance of A and B below H is indicated on the V projection. Thus if to A∧h B∧h the perpendiculars A∧h A;and;r and B∧h B∧r be drawn, A∧r B∧r will be the true length of A B." —French, 1911

Construction of Geometric Revolution

"The distance of A and B below H is indicated on the V projection. Thus if to A∧h B∧h the perpendiculars…

"The H projection of the line AB in the space is a line connecting the feet of all the perpendiculars from AB to the plane. These perpendiculars form what is known as the projecting plane. If this projecting plane to be revolved about its H trace, which is the H projection of the line, until it coincides with H, the line will be seen in its true length." —French, 1911

Revolutions into the Plane of Geometric Shapes

"The H projection of the line AB in the space is a line connecting the feet of all the perpendiculars…

"A block revolved from its first position about an axis perpendicular to H through 45 degrees, then about an axis perpendicular to P through 45 degrees until the cut face MNO is parallel to the vertical plane. To avoid confusion it is well to letter or number the corresponding points as the views are carried along." —French, 1911

Successive Revolutions of Geometric Shapes

"A block revolved from its first position about an axis perpendicular to H through 45 degrees, then…

Illustration of 2 ladders leaning against opposite sides of a palm tree to form similar right triangles. The angles of elevation from the ground to where the ladders meet the tree are congruent. Illustration can be used for problems involving proportions.

2 Ladders Leaning Against a Tree

Illustration of 2 ladders leaning against opposite sides of a palm tree to form similar right triangles.…

Illustration of 3 ladders leaning against the side of a building (wall) to form right triangles. The distance from the base of the ladders to the wall is the same for all three ladders.

3 Ladders Leaning Against a Wall

Illustration of 3 ladders leaning against the side of a building (wall) to form right triangles. The…

Illustration of a lever with fulcrum F. W represents the weight lifted, P is the force that does the lifting, D is the distance from the fulcrum to the point of application of the force, and d is the distance from the fulcrum to the point where the weight is attached. In all possible relations of the fulcrum, weight, and force the following proportion holds: P:W = d:D.

Lever and Fulcrum

Illustration of a lever with fulcrum F. W represents the weight lifted, P is the force that does the…

Illustration of a hammer being used as a lever. F represents the fulcrum.

Hammer Used as a Lever

Illustration of a hammer being used as a lever. F represents the fulcrum.

Illustration of an ordinary steel-yard being used as a lever. F represents the fulcrum. Weight P is used to balance weight W.

Steel-yard Used as a Lever

Illustration of an ordinary steel-yard being used as a lever. F represents the fulcrum. Weight P is…

Illustration that shows if two parallel lines are cut by three or more transversals that pass through the same point, the corresponding segments are proportional.

Parallel Lines Cut by Transversals

Illustration that shows if two parallel lines are cut by three or more transversals that pass through…

Illustration that shows if two parallel lines are cut by three or more transversals that pass through the same point, the corresponding segments are proportional.

Parallel Lines Cut by Transversals

Illustration that shows if two parallel lines are cut by three or more transversals that pass through…

A man measuring the height of a tree by determining the angle and how far away he is standing.

Measuring Tree Height

A man measuring the height of a tree by determining the angle and how far away he is standing.

Illustration of 2 similar pentagons.

Similar Pentagons

Illustration of 2 similar pentagons.

Illustration of 2 similar pentagons.

Similar Pentagons

Illustration of 2 similar pentagons.

Illustration that shows similar polygons (pentagons) that can be used to show proportionality.

Similar Polygons (Pentagons) That Can Be Used To Show Proportionality

Illustration that shows similar polygons (pentagons) that can be used to show proportionality.

Illustration that shows similar polygons (pentagons) that can be used to show proportionality.

Similar Polygons (Pentagons) That Can Be Used To Show Proportionality

Illustration that shows similar polygons (pentagons) that can be used to show proportionality.

Illustration of a hydraulic machine. "A principle known as Pascal's Law states that pressure exerted on a liquid in a closed vessel is transmitted equally and undiminished in all directions." If a, A, p, and P respectively represent the areas and pressures, then the following proportion holds: a:A = p:P.

Hydraulic Machine Exerting Pressure

Illustration of a hydraulic machine. "A principle known as Pascal's Law states that pressure exerted…

The illustration showing the projection of the triangles from the triangle pyramid as shown on top. This projection helps create the development of the pyramid by connecting each projection together.

Triangle Pyramid Side Projections

The illustration showing the projection of the triangles from the triangle pyramid as shown on top.…

Illustration to show that an angle bisector of a triangle divides the opposite side into segments which are proportional to the adjacent sides.

Angle Bisector of Triangle Dividing Opposite Side Into Proportionate Segments

Illustration to show that an angle bisector of a triangle divides the opposite side into segments which…

Illustration to show that a bisector of a an exterior angle of a triangle divides the opposite side into segments which are proportional to the adjacent sides.

Exterior Angle Bisector of Triangle Dividing Opposite Side Into Proportionate Segments

Illustration to show that a bisector of a an exterior angle of a triangle divides the opposite side…

Illustration to show that if parallel lines are cut by any number of parallels, the corresponding intercepts are proportional.

Parallel Lines Cut by Parallels, Corresponding Intercepts Proportional

Illustration to show that if parallel lines are cut by any number of parallels, the corresponding intercepts…

Illustration to show that if a line is drawn through two sides of a triangle parallel to the third side, it divides those sides proportionally.

Triangle Divided by Parallel Lines to Form Proportionate Triangles

Illustration to show that if a line is drawn through two sides of a triangle parallel to the third side,…

Illustration to show that if a line divides two sides of a triangle proportionally, it is parallel to the third side.

Triangle Divided by Parallel Lines to Form Proportionate Triangles

Illustration to show that if a line divides two sides of a triangle proportionally, it is parallel to…

"The pyramid be revolved about an axis perpendicular to V, the front view will be unchanged and may be copied in the new position distance from the ground line to any point in the top view be unchanged, hence the new top view may be found by projecting up from the front view and across from the original top view" —French, 1911

Revolution About Axis Forward or Back

"The pyramid be revolved about an axis perpendicular to V, the front view will be unchanged and may…

The object can revolve around an axis (H) to create a projection on the other plane without changing the size, shape, and dimensions.

Revolution About Axis Perpendicular to H

The object can revolve around an axis (H) to create a projection on the other plane without changing…

"The pyramid be revolved about an axis perpendicular to V, the front view will be unchanged and may be copied in the new position distance from the ground line to any point in the top view be unchanged, hence the new top view may be found by projecting up from the front view and across from the original top view" —French, 1911

Revolution About Axis Perpendicular to V

"The pyramid be revolved about an axis perpendicular to V, the front view will be unchanged and may…

Illustration of a palm tree that is perpendicular to the ground. The tree is perfectly straight, as is the ground. This drawing could be used for shadow, proportion, trigonometric, or Pythagorean Theorem problems.

Palm Tree Perpendicular to Ground

Illustration of a palm tree that is perpendicular to the ground. The tree is perfectly straight, as…

Triangle diagram for measuring heights of trees using proportions.

Using Proportions To Find Heights of Trees

Triangle diagram for measuring heights of trees using proportions.

Triangle diagram for measuring heights of trees using proportions

Using Proportions To Find Heights of Trees

Triangle diagram for measuring heights of trees using proportions

Right triangle inscribed in semicircle. Illustration shows that the perpendicular from any point in the circumference to the diameter of a circle is the mean proportional between the segments of the diameter.

Right Triangle Inscribed in Semicircle Shows Mean Proportional

Right triangle inscribed in semicircle. Illustration shows that the perpendicular from any point in…

Illustration that shows two mutually equiangular triangles are similar.

Mutually Equiangular Similar Triangles

Illustration that shows two mutually equiangular triangles are similar.

Illustration that shows that two triangles which have their sides respectively parallel, or respectively perpendicular, are similar.

Similar Triangles With Respective Sides Parallel or Perpendicular

Illustration that shows that two triangles which have their sides respectively parallel, or respectively…

Illustration of 2 similar triangles with altitudes drawn.

Similar triangles

Illustration of 2 similar triangles with altitudes drawn.

Illustration of two similar triangles, abc and ABC.

Similar Triangles

Illustration of two similar triangles, abc and ABC.

Illustration of a triangle divided by a parallel line to form two similar triangles.

Similar Triangles

Illustration of a triangle divided by a parallel line to form two similar triangles.

Illustration of similar triangles used to find distance across a lake.

Similar Triangles for Distance Across Lake

Illustration of similar triangles used to find distance across a lake.

Illustration of similar triangles used to find distance across a stream

Similar Triangles for Distance Across Stream

Illustration of similar triangles used to find distance across a stream

Illustration of similar triangles used to find height of smokestack.

Similar Triangles for Height of Smokestack

Illustration of similar triangles used to find height of smokestack.

Illustration that shows two similar triangles with altitudes drawn.

Similar Triangles With Altitudes Drawn

Illustration that shows two similar triangles with altitudes drawn.