ClipArt ETC

This mathematics ClipArt gallery offers 127 images that can be used to demonstrate various geometric theorems and proofs.

Diagram used to prove the theorem: "The opposite faces of a parallelopiped are equal and parallel."

Equal and Parallel Opposite Faces of a Parallelopiped

Diagram used to prove the theorem: "The opposite faces of a parallelopiped are equal and parallel."

Diagram used to prove the theorem: "The rectangular parallelopipeds which have two dimensions in common are to each other as their third dimension."

Relationship Between 2 Parallelopipeds With Equal Altitudes

Diagram used to prove the theorem: "The rectangular parallelopipeds which have two dimensions in common…

Diagram used to prove the theorem: "The rectangular parallelopipeds are to each other as the product of their three dimensions."

Relationship Between Dimensions of Parallelopipeds

Diagram used to prove the theorem: "The rectangular parallelopipeds are to each other as the product…

Diagram used to prove the theorem: "The volume of a any parallelopiped is equal to the product of its base and its altitude."

Volume of Parallelopiped

Diagram used to prove the theorem: "The volume of a any parallelopiped is equal to the product of its…

Diagram used to prove the theorem: "The volume of a rectangular parallelopiped is equal to the product of its three dimensions."

Volume of Rectangular Parallelopiped

Diagram used to prove the theorem: "The volume of a rectangular parallelopiped is equal to the product…

A line moves in a plane and it therefore envelopes a plane curve.

Plane Curve

A line moves in a plane and it therefore envelopes a plane curve.

"If two intersecting planes are each perpendicular to a third plane, their intersection is also perpendicular to that plane."

2 Intersecting Planes Perpendicular To A Third Plane

"If two intersecting planes are each perpendicular to a third plane, their intersection is also perpendicular…

"If a straight line is perpendicular to each of two straight lines at their point of intersection it is perpendicular to the plane of those lines."

Line Perpendicular To Plane

"If a straight line is perpendicular to each of two straight lines at their point of intersection it…

"If one of two parallels is perpendicular to a plane, the other is also."

Lines Perpendicular To A Plane

"If one of two parallels is perpendicular to a plane, the other is also."

"Through a given line oblique to a plane, one, and only one plane, can be passed perpendicular to the given plane."

Plane Passed Perpendicular To A Given Plane

"Through a given line oblique to a plane, one, and only one plane, can be passed perpendicular to the…

Diagram used to prove the theorem: "If a pyramid is cut by a plane parallel to the base, the edges are divided proportionally, and the section is a polygon similar to the base."

Pyramid Cut By Plane

Diagram used to prove the theorem: "If a pyramid is cut by a plane parallel to the base, the edges are…

Diagram used to prove the theorem: "Every section of a sphere by a lane is a circle."

Sphere Cut By Plane

Diagram used to prove the theorem: "Every section of a sphere by a lane is a circle."

Diagram used to prove the theorem: "A plane perpendicular to a radius at its extremity is tangent to the sphere."

Sphere Tangent to Plane

Diagram used to prove the theorem: "A plane perpendicular to a radius at its extremity is tangent to…

Illustration of three intersecting planes. "The intersections of two parallel planes by a third plane are parallel lines."

3 Intersecting Planes

Illustration of three intersecting planes. "The intersections of two parallel planes by a third plane…

Illustration of three intersecting planes. "The straight line perpendicular to one of two parallel lanes is perpendicular to the other."

3 Intersecting Planes

Illustration of three intersecting planes. "The straight line perpendicular to one of two parallel lanes…

"If two straight lines are cut by three parallel planes, the corresponding segments are proportional."

3 Parallel Planes

"If two straight lines are cut by three parallel planes, the corresponding segments are proportional."

"If two angles not in the same plane have their sides respectively parallel and lying in the same direction, they are equal and their planes are parallel."

Angles In Parallel Planes

"If two angles not in the same plane have their sides respectively parallel and lying in the same direction,…

"If two intersecting lines are each parallel to a given plane, the plane of these lines is parallel to the given plane."

Parallel Planes

"If two intersecting lines are each parallel to a given plane, the plane of these lines is parallel…

"If two planes are perpendicular to each other, a line in one of them perpendicular to the intersection is perpendicular to the other."

Perpendicular Planes

"If two planes are perpendicular to each other, a line in one of them perpendicular to the intersection…

Diagram used to prove the theorem: "Two similar polyhedrons may be decomposed into the same number of tetrahedrons, similar each to each , and similarly placed."

Two Similar Polyhedrons

Diagram used to prove the theorem: "Two similar polyhedrons may be decomposed into the same number of…

Diagram used to prove the theorem: "The lateral area of a prism is equal to the product of a lateral edge by the perimeter of a right section."

Lateral Area of A Prism

Diagram used to prove the theorem: "The lateral area of a prism is equal to the product of a lateral…

Diagram used to prove the theorem: "The volume of a prismatoid is equal to the product of one-sixth the altitude into the sum of the two bases and four times the mid-section."

Volume of Prismatoid

Diagram used to prove the theorem: "The volume of a prismatoid is equal to the product of one-sixth…

Diagram used to prove the theorem: "Two prisms are equal when the three faces about a trihedral of one are equal respectively to the three faces about a trihedral of the other, and similarly arranged."

Two Equal Prisms

Diagram used to prove the theorem: "Two prisms are equal when the three faces about a trihedral of one…

Illustration used to prove "Two angles whose sides are perpendicular each to each are either equal or supplementary."

Angles With Perpendicular Sides Are Equal or Supplementary Proof

Illustration used to prove "Two angles whose sides are perpendicular each to each are either equal or…

Illustration used to prove the Pythagorean Theorem, according to Euclid. A perpendicular is drawn from the top vertex of the right triangle extended through the bottom square, forming 2 rectangles. Each rectangle has the same area as one of the two legs. This proves that the sum of the squares of the legs is equal to the square of the hypotenuse (Pythagorean Theorem).

Euclid's Pythagorean Theorem Proof

Illustration used to prove the Pythagorean Theorem, according to Euclid. A perpendicular is drawn from…

Illustration used to prove "An exterior angle of a triangle is equal to the sum of the two remote interior angles."

Exterior Angle Proof

Illustration used to prove "An exterior angle of a triangle is equal to the sum of the two remote interior…

Illustration that can be used to prove the Pythagorean Theorem, the sum of the squares of the legs is equal to the square of the hypotenuse.

Geometric Pythagorean Theorem Proof

Illustration that can be used to prove the Pythagorean Theorem, the sum of the squares of the legs is…

Illustration that can be used to prove the Pythagorean Theorem, the sum of the squares of the legs is equal to the square of the hypotenuse. The geometrical illustration depicts a 3,4,5 right triangle with the square units drawn to prove that the sum of the squares of the legs (9 + 16) equals the square of the hypotenuse.

Geometric Pythagorean Theorem Proof

Illustration that can be used to prove the Pythagorean Theorem, the sum of the squares of the legs is…

A visual illustration used to prove the Pythagorean Theorem by rearrangement. When the 4 identical triangles are removed, the areas are equal. Thus, proving the sum of the squares of the legs is equal to the square of the hypotenuse.

Pythagorean Theorem Proof by Rearrangement

A visual illustration used to prove the Pythagorean Theorem by rearrangement. When the 4 identical triangles…

Illustration used to prove "If the sides of any polygon are prolonged in succession one way, no two adjacent sides being prolonged through the same vertex, the sum of the exterior angles thus formed is four right angles."

Sum of Exterior Angles of a Polygon Proof

Illustration used to prove "If the sides of any polygon are prolonged in succession one way, no two…

Illustration used to prove "The sum of all the angles of any polygon is twice as many right angles as the polygon has sides, less four right angles."

Sum of Interior Angles of a Polygon Proof

Illustration used to prove "The sum of all the angles of any polygon is twice as many right angles as…

An illustration showing a model that illustrates the Pythagorean Theorem: a&sup2 + b&sup2 = c&sup2.

Model Of Pythagorean Theorem

An illustration showing a model that illustrates the Pythagorean Theorem: a² + b² = c².

An illustration showing that the area of a regular polygon is equal to the area of a triangle whose base is equal to the sum of all the sides, and the height a equal to the appotem of the polygon. "The reason of this is that the area of two or more triangles ABC and ADC having a common or equal base b and equal height h are alike."

Area Of Regular Polygon Proof

An illustration showing that the area of a regular polygon is equal to the area of a triangle whose…

Illustration used to show "If one acute angle of a right triangle is double the other, the hypotenuse is double the shorter side."

Relationships In A Right Triangle

Illustration used to show "If one acute angle of a right triangle is double the other, the hypotenuse…

Five points are given, of which not three are in a line, a curve of second order may be drawn through all of them.

Second Order Curve

Five points are given, of which not three are in a line, a curve of second order may be drawn through…

Illustration of a circle used to prove "Any angle inscribed in a semicircle is a right angle."

Right Angles Inscribed in Semicircle Proof

Illustration of a circle used to prove "Any angle inscribed in a semicircle is a right angle."

Illustration used to prove "The line bisecting one side of a triangle and parallel to another side bisects the third side."

Line Bisecting Side of a Triangle

Illustration used to prove "The line bisecting one side of a triangle and parallel to another side bisects…

Diagram used to prove the theorem: "All points in the circumference of a circle of a sphere are equally distant from each of its poles."

Circumference of a Circle of a Sphere

Diagram used to prove the theorem: "All points in the circumference of a circle of a sphere are equally…

Diagram used to prove the theorem: "A spherical angle is measured by the arc of a great circle described from its vertex as a ole and included between its sides (produced if necessary)."

Measure of a Spherical Angle

Diagram used to prove the theorem: "A spherical angle is measured by the arc of a great circle described…

Diagram used to prove the theorem: "The volume of a spherical segment is equal to the sum of two cylinders and a sphere, the altitudes of the cylinders being one half the altitude of the segment, and their bases the upper and lower bases of the segment, respectively, and the diameter of the sphere being the altitude of the segment."

Volume of Spherical Segment

Diagram used to prove the theorem: "The volume of a spherical segment is equal to the sum of two cylinders…

Diagram used to prove the theorem: "The area of a spherical triangle, expressed in spherical degrees, is equal to its spherical excess expressed in angular degrees."

Area of Spherical Triangle

Diagram used to prove the theorem: "The area of a spherical triangle, expressed in spherical degrees,…

Diagram used to prove the theorem: "In a spherical triangle, the greater side is opposite the greater angle, and conversely."

Side Comparison of Spherical Triangle

Diagram used to prove the theorem: "In a spherical triangle, the greater side is opposite the greater…

Diagram used to prove the theorem: "Between two straight lines not in the same plane only one perpendicular can be drawn."

Perpendicular Between 2 Straight Lines

Diagram used to prove the theorem: "Between two straight lines not in the same plane only one perpendicular…

Diagram used to prove the theorem: "The area of the surface generated by a straight line revolving about an axis in its plane is equal to the product of the projection of the line on the axis by the circumference whose radius is perpendicular erected at the middle point of the line and terminated by the axis."

Area of Surface Generated by a Straight Line

Diagram used to prove the theorem: "The area of the surface generated by a straight line revolving about…

Diagram used to prove the theorem: "Two tetrahedrons having a trihedral angle in each equal, are to each other as the products of the including edges."

Two Proportional Tetrahedrons

Diagram used to prove the theorem: "Two tetrahedrons having a trihedral angle in each equal, are to…

Illustration used to prove the theorem, "Two angles whose sides are parallel, each to each, are either equal or supplementary."

2 Angles With Parallel Sides Theorem

Illustration used to prove the theorem, "Two angles whose sides are parallel, each to each, are either…

Illustration used to prove the theorem, "Two angles whose sides are perpendicular, each to each, are either equal or supplementary."

2 Angles With Perpendicular Sides Theorem

Illustration used to prove the theorem, "Two angles whose sides are perpendicular, each to each, are…

Illustration used to prove that "If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second."

2 Triangles Theorem

Illustration used to prove that "If two triangles have two sides of one equal respectively to two sides…

Illustration used to prove that "If two triangles have two sides of one equal respectively to two sides of the other, but the third side of the first greater than the third side of the second, then the angle opposite the third side of the first is greater than the angle opposite the third side of the second."

2 Triangles Theorem

Illustration used to prove that "If two triangles have two sides of one equal respectively to two sides…

Illustration used to prove that "If one side of a triangle is prolonged, the exterior angle formed is greater than either of the remote interior angles."

Exterior Angle of Triangle Theorem

Illustration used to prove that "If one side of a triangle is prolonged, the exterior angle formed is…

Illustration used to prove that "If two straight lines are parallel to a third straight line, they are parallel to each other."

Parallel Lines Theorem

Illustration used to prove that "If two straight lines are parallel to a third straight line, they are…

Illustration used to prove that "If two sides of a triangle are unequal, the angle opposite the greater side is greater than the angle opposite the less side."

Sides of Triangle Theorem

Illustration used to prove that "If two sides of a triangle are unequal, the angle opposite the greater…

Illustration used to prove that "The sum of any two sides of a triangle is greater than the third side."

Sides of Triangle Theorem

Illustration used to prove that "The sum of any two sides of a triangle is greater than the third side."

Illustration used to prove the theorem, "The sum of the angles of any triangle is two right angles."

Sum Of Angles In Triangle Theorem

Illustration used to prove the theorem, "The sum of the angles of any triangle is two right angles."

Illustration used to prove the theorem, "If two straight lines are cut by a transversal making a pair of alternate interior angles equal, the lines are parallel."

Parallel Lines Cut By A Transversal Theorem

Illustration used to prove the theorem, "If two straight lines are cut by a transversal making a pair…

Illustration used to prove the theorem, "If two parallel lines are cut by a transversal, the alternate interior angles are equal."

Parallel Lines Cut By A Transversal Theorem

Illustration used to prove the theorem, "If two parallel lines are cut by a transversal, the alternate…

Illustration used to prove the theorem "The line bisecting one of the non parallel sides of a trapezoid and parallel to the bases bisects the other of the non parallel sides also."

Line Bisecting Trapezoid Sides

Illustration used to prove the theorem "The line bisecting one of the non parallel sides of a trapezoid…

Illustration used to show "The altitudes of a triangle are concurrent."

Altitudes In A Triangle

Illustration used to show "The altitudes of a triangle are concurrent."

Illustration used to prove "The bisectors of the angles of a triangle are concurrent in a point which is equidistant from the three sides of the triangle."

Angle Bisectors In A Triangle

Illustration used to prove "The bisectors of the angles of a triangle are concurrent in a point which…

Illustration used to show "Any two medians of a triangle intersect each other in a trisection point of each."

Medians In A Triangle

Illustration used to show "Any two medians of a triangle intersect each other in a trisection point…