ClipArt ETC
A balance scale holding 5 pounds on the left and 3 and 2 pound weights on the right showing 3+2=5.

Addition Scale

A balance scale holding 5 pounds on the left and 3 and 2 pound weights on the right showing 3+2=5.

Illustration of 2 equal dihedral angles.

Two Equal Dihedral Angles

Illustration of 2 equal dihedral angles.

Illustration of 3 equal dihedral angles. "Two dihedral angles have the same ratio as their plane angles."

Equal Dihedral Angles

Illustration of 3 equal dihedral angles. "Two dihedral angles have the same ratio as their plane angles."

Illustration used to prove that all right angles are equal.

Equal Right Angles

Illustration used to prove that all right angles are equal.

An illustration showing when one straight line meets another straight line and makes the adjacent angles equal, each of these angles is called a right angle.

Right Angles With Same Vertex

An illustration showing when one straight line meets another straight line and makes the adjacent angles…

Diagram used to prove the theorem: "Two trihedral angles, which have three face angles of the one equal respectively to three face angles of the other , are either equal or symmetrical."

Symmetrical or Equal Trihedral Angles

Diagram used to prove the theorem: "Two trihedral angles, which have three face angles of the one equal…

Illustration of two angles whose sides are parallel, each to each, to show they are either equal or supplementary.

Angles With Parallel Sides

Illustration of two angles whose sides are parallel, each to each, to show they are either equal or…

"It is evident that, when a solid is immersed in a fluid, it will displace exactly its own volume of the fluid. Immerse a solid cube one centimeter on each edge in water, so that its upper face shall be level and one centimeter below the surface of the liquid, as shown. The lateral pressures upon any two opposite vertical surfaces of the cube, as a and b, are clearly equal and opposite." -Avery 1895

Archimedies Principle

"It is evident that, when a solid is immersed in a fluid, it will displace exactly its own volume of…

"The balance is essentially a lever of the first class, having equal arms. The beam carries a pan at each end, one for the weidhts used, the other for the article to be weighed." -Avery 1895

Balance

"The balance is essentially a lever of the first class, having equal arms. The beam carries a pan at…

"When bodies of equal weight are supported by the arms of a lever, they will balance each other when placed at equal distances from the fulcrum." —Quackenbos 1859

Balance

"When bodies of equal weight are supported by the arms of a lever, they will balance each other when…

Method to bisect an angle

Bisect An Angle

Method to bisect an angle

Illustration used to show that "If two tangents are drawn from any given point to a circle, those tangents are equal."

Equal Tangents to Circle Theorem

Illustration used to show that "If two tangents are drawn from any given point to a circle, those tangents…

Illustration of a circle with equal chords, which are equally distant from the center.

Circle With Equal Chords

Illustration of a circle with equal chords, which are equally distant from the center.

Illustration of equal circles to show that two central angles have the same ratio as their intercepted arcs.

Equal Circles With Intercepted Arcs

Illustration of equal circles to show that two central angles have the same ratio as their intercepted…

"A cube is a prism whose faces are ends are squares. All the faces of a cube are equal." —Hallock 1905

Cube

"A cube is a prism whose faces are ends are squares. All the faces of a cube are equal." —Hallock…

Illustration of 108 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

108 Stacked Congruent Cubes

Illustration of 108 congruent cubes stacked at various heights. A 3-dimensional representation on a…

Illustration of 117 congruent cubes stacked in columns of one, four, and six. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

117 Stacked Congruent Cubes

Illustration of 117 congruent cubes stacked in columns of one, four, and six. A 3-dimensional representation…

Illustration of 128 congruent cubes stacked so they form a rectangular solid that measures 4 by 4 by 8. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

128 Stacked Congruent Cubes

Illustration of 128 congruent cubes stacked so they form a rectangular solid that measures 4 by 4 by…

Illustration of 132 congruent cubes stacked in 22 columns of 6 in the shape of a U. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

132 Stacked Congruent Cubes

Illustration of 132 congruent cubes stacked in 22 columns of 6 in the shape of a U. A 3-dimensional…

Illustration of 154 congruent cubes stacked in columns increasing from one to four. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

154 Stacked Congruent Cubes

Illustration of 154 congruent cubes stacked in columns increasing from one to four. A 3-dimensional…

Illustration of 16 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

16 Stacked Congruent Cubes

Illustration of 16 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional…

Illustration of 17 congruent cubes stacked in ones and twos in the shape of a V. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

17 Stacked Congruent Cubes

Illustration of 17 congruent cubes stacked in ones and twos in the shape of a V. A 3-dimensional representation…

Illustration of two congruent cubes that are tangent along an edge. A 3-dimensional representation on a 2-dimensional surface.

2 Congruent Cubes

Illustration of two congruent cubes that are tangent along an edge. A 3-dimensional representation on…

Illustration of 20 congruent cubes stacked in twos and threes. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

20 Stacked Congruent Cubes

Illustration of 20 congruent cubes stacked in twos and threes. A 3-dimensional representation on a 2-dimensional…

Illustration of 20 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

20 Stacked Congruent Cubes

Illustration of 20 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional…

Illustration of 20 congruent cubes stacked at heights increasing from 1 to 4 cubes. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

20 Stacked Congruent Cubes

Illustration of 20 congruent cubes stacked at heights increasing from 1 to 4 cubes. A 3-dimensional…

Illustration of 22 congruent cubes stacked in ones, twos, and threes. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

22 Stacked Congruent Cubes

Illustration of 22 congruent cubes stacked in ones, twos, and threes. A 3-dimensional representation…

Illustration of 22 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

22 Stacked Congruent Cubes

Illustration of 22 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional…

Illustration of 24 congruent cubes stacked at various heights to resemble steps. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

24 Stacked Congruent Cubes

Illustration of 24 congruent cubes stacked at various heights to resemble steps. A 3-dimensional representation…

Illustration of 256 congruent cubes stacked so they form 4 larger cubes that measures 4 by 4 by 4 each. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

256 Stacked Congruent Cubes

Illustration of 256 congruent cubes stacked so they form 4 larger cubes that measures 4 by 4 by 4 each.…

Illustration of 27 congruent cubes stacked to resemble a larger cube that measures three by three by three cubes. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

27 Stacked Congruent Cubes

Illustration of 27 congruent cubes stacked to resemble a larger cube that measures three by three by…

Illustration of 27 congruent cubes stacked at various heights in the shape of a W. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

27 Stacked Congruent Cubes

Illustration of 27 congruent cubes stacked at various heights in the shape of a W. A 3-dimensional representation…

Illustration of 28 congruent cubes placed in the shape of a square. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

28 Congruent Cubes Placed in the Shape of a Square

Illustration of 28 congruent cubes placed in the shape of a square. A 3-dimensional representation on…

Illustration of 30 congruent cubes stacked in decreasing heights. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

30 Stacked Congruent Cubes

Illustration of 30 congruent cubes stacked in decreasing heights. A 3-dimensional representation on…

Illustration of 33 congruent cubes stacked at various heights in a zigzag pattern. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

33 Stacked Congruent Cubes

Illustration of 33 congruent cubes stacked at various heights in a zigzag pattern. A 3-dimensional representation…

Illustration of 35 congruent cubes stacked in ones and twos in the shape of a W. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

35 Stacked Congruent Cubes

Illustration of 35 congruent cubes stacked in ones and twos in the shape of a W. A 3-dimensional representation…

Illustration of 35 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

35 Stacked Congruent Cubes

Illustration of 35 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional…

Illustration of 36 congruent cubes stacked at various heights with outer edges forming a square. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

36 Stacked Congruent Cubes

Illustration of 36 congruent cubes stacked at various heights with outer edges forming a square. A 3-dimensional…

Illustration of 36 congruent cubes stacked to resemble a 1 by 1 by 1 cube on a 2 by 2 by 2 cube on a 3 by 3 by 3 cube. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

36 Stacked Congruent Cubes

Illustration of 36 congruent cubes stacked to resemble a 1 by 1 by 1 cube on a 2 by 2 by 2 cube on a…

Illustration of 39 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

39 Stacked Congruent Cubes

Illustration of 39 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional…

Illustration of 4 congruent cubes stacked in ones and twos. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

4 Stacked Congruent Cubes

Illustration of 4 congruent cubes stacked in ones and twos. A 3-dimensional representation on a 2-dimensional…

Illustration of 50 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

50 Stacked Congruent Cubes

Illustration of 50 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional…

Illustration of 56 congruent cubes stacked in twos in the shape of a square. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

56 Stacked Congruent Cubes

Illustration of 56 congruent cubes stacked in twos in the shape of a square. A 3-dimensional representation…

Illustration of 56 congruent cubes stacked in heights of 1, 4, and 5 cubes that form a zigzag pattern. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

56 Stacked Congruent Cubes

Illustration of 56 congruent cubes stacked in heights of 1, 4, and 5 cubes that form a zigzag pattern.…

Illustration of 57 congruent cubes stacked in heights of 1 and 5 cubes that form a zigzag pattern. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

57 Stacked Congruent Cubes

Illustration of 57 congruent cubes stacked in heights of 1 and 5 cubes that form a zigzag pattern. A…

Illustration of 59 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

59 Stacked Congruent Cubes

Illustration of 59 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional…

Illustration of 64 congruent cubes stacked so they form a cube that measures 4 by 4 by 4. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

64 Stacked Congruent Cubes

Illustration of 64 congruent cubes stacked so they form a cube that measures 4 by 4 by 4. A 3-dimensional…

Illustration of 65 congruent cubes stacked at heights increasing from 1 to 5 cubes. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

65 Stacked Congruent Cubes

Illustration of 65 congruent cubes stacked at heights increasing from 1 to 5 cubes. A 3-dimensional…

Illustration used to prove that triangle EFD is equilateral given that triangle ABC is equilateral and AE=BF=CD.

Equilateral Triangle Inscribed In An Equilateral Triangle

Illustration used to prove that triangle EFD is equilateral given that triangle ABC is equilateral and…

A flashcard featuring a math symbol for Approximately Equal To

Flashcard of a math symbol for Approximately Equal To

A flashcard featuring a math symbol for Approximately Equal To

A flashcard featuring a math symbol for Equal To

Flashcard of a math symbol for Equal To

A flashcard featuring a math symbol for Equal To

Illustration showing that if two angles of a triangle are equal, the bisectors of these angles are equal.

Angle Bisectors In An Isosceles Triangle

Illustration showing that if two angles of a triangle are equal, the bisectors of these angles are equal.

Illustration showing that can be used to prove that the base angles of an isosceles triangle are equal.

Base Angles In An Isosceles Triangle

Illustration showing that can be used to prove that the base angles of an isosceles triangle are equal.

Illustration showing that if equal segments measured from the vertex are laid off on the arms of an isosceles triangle, the lines joining the ends of these segments to the opposite ends of the base will be equal.

Equal Segments In An Isosceles Triangle

Illustration showing that if equal segments measured from the vertex are laid off on the arms of an…

Illustration showing that if equal segments prolonged through the vertex are laid off on the arms of an isosceles triangle, the lines joining the ends of these segments to the opposite ends of the base will be equal.

Equal Segments In An Isosceles Triangle

Illustration showing that if equal segments prolonged through the vertex are laid off on the arms of…

Illustration showing that if equal segments measured from the end of the base are laid off on the base of an isosceles triangle, the lines joining the vertex of the triangle to the ends of the segments will be equal.

Equal Segments In An Isosceles Triangle

Illustration showing that if equal segments measured from the end of the base are laid off on the base…

Illustration showing that if equal segments measured from the end of the base prolonged are laid off on the base of an isosceles triangle, the lines joining the vertex of the triangle to the ends of the segments will be equal.

Equal Segments In An Isosceles Triangle

Illustration showing that if equal segments measured from the end of the base prolonged are laid off…

Illustration of two straight lines drawn from a point in a perpendicular to a given line, cutting off on the given line equal segments from the foot of the perpendicular, are equal and make equal angles with the perpendicular. This illustration can be used to show the proof.

Lines Drawn to Another Line to Form Triangle

Illustration of two straight lines drawn from a point in a perpendicular to a given line, cutting off…

Illustration of two parallel lines with equal segments between them. Two parallel lines are everywhere equally distant.

Parallel Lines With Equal Segments Between

Illustration of two parallel lines with equal segments between them. Two parallel lines are everywhere…

Illustration showing two parallel vertical lines cut by a perpendicular line and a transversal. Congruent line segments are marked.

Parallel Lines Cut By a Perpendicular And Transversal

Illustration showing two parallel vertical lines cut by a perpendicular line and a transversal. Congruent…