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…

Method to bisect an angle

Bisect An Angle

Method to bisect an angle

Equal circles inside and tangent to the outside circle, also tangent to each other

Circle to Circle Tangents

Equal circles inside and tangent to the outside circle, also tangent to each other

Six equal circles tangent to each other and to the sides of the triangle

Circle Triangle Tangents

Six equal circles tangent to each other and to the sides of the triangle

Circular rosette-like pattern made with 12 overlapping congruent circles tangent to a center circle and an outer circle.

12 Overlapping Circles About a Center Circle and Inside a Larger Circle

Circular rosette-like pattern made with 12 overlapping congruent circles tangent to a center circle…

2 congruent circles whose intersection includes a tangent circle with diameter equal to the radii of the larger circles.

2 Intersecting Circles

2 congruent circles whose intersection includes a tangent circle with diameter equal to the radii of…

Circular rosette-like pattern made with 24 overlapping congruent circles tangent to a center circle and an outer circle.

24 Overlapping Circles About a Center Circle and Inside a Larger Circle

Circular rosette-like pattern made with 24 overlapping congruent circles tangent to a center circle…

Circular rosette-like pattern made with 48 overlapping congruent circles tangent to a center circle and an outer circle.

48 Overlapping Circles About a Center Circle and Inside a Larger Circle

Circular rosette-like pattern made with 48 overlapping congruent circles tangent to a center circle…

A regular hexagon containing 7 congruent circles. The circles are externally tangent to each other and internally tangent to the hexagon.

7 Congruent Circles In A Regular Hexagon

A regular hexagon containing 7 congruent circles. The circles are externally tangent to each other and…

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 of 3 right congruent tangent circular cylinders.  The height of all the cylinders is greater than the diameter of the base.

3 Congruent Tangent Right Circular Cylinders

Illustration of 3 right congruent tangent circular cylinders. The height of all the cylinders is greater…

Illustration of 3 right congruent tangent circular cylinders.

3 Congruent Tangent Right Circular Cylinders

Illustration of 3 right congruent tangent circular cylinders.

Illustration of 3 right congruent tangent circular cylinders.  The height of all the cylinders is greater than the diameter of the base.

3 Congruent Tangent Right Circular Cylinders

Illustration of 3 right congruent tangent circular cylinders. The height of all the cylinders is greater…

Illustration of 4 congruent tangent right circular cylinders. The height of all the cylinders is greater than the diameter of the base.

4 Congruent Tangent Right Circular Cylinders

Illustration of 4 congruent tangent right circular cylinders. The height of all the cylinders is greater…

Illustration of 16 concentric congruent ellipses that are rotated about the center at equal intervals of 22.5°. The ellipses are externally tangent to the circle in which they are inscribed.

16 Rotated Concentric Ellipses

Illustration of 16 concentric congruent ellipses that are rotated about the center at equal intervals…

Illustration of 2 concentric congruent ellipses that are rotated about the center at 90°. The ellipses are externally tangent to the circle in which they are inscribed.

2 Rotated Concentric Ellipses

Illustration of 2 concentric congruent ellipses that are rotated about the center at 90°. The ellipses…

Illustration of 4 concentric congruent ellipses that are rotated about the center at equal intervals of 45°. The ellipses are externally tangent to the circle in which they are inscribed.

4 Rotated Concentric Ellipses

Illustration of 4 concentric congruent ellipses that are rotated about the center at equal intervals…

Illustration of 8 concentric congruent ellipses that are rotated about the center at equal intervals of 22.5°. The ellipses are externally tangent to the circle in which they are inscribed.

8 Rotated Concentric Ellipses

Illustration of 8 concentric congruent ellipses that are rotated about the center at equal intervals…

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

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…

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.

A flashcard featuring a math symbol for Congruent To

Flashcard of a math symbol for Congruent To

A flashcard featuring a math symbol for Congruent To

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 used to prove the theorem "Two parallelograms are equal if two sides and the included angle of one are equal respectively to two sides and the included angle of the other."

2 Equal Parallelograms

Illustration used to prove the theorem "Two parallelograms are equal if two sides and the included angle…

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…

Illustration of 2 right octagonal prisms with congruent bases, but different heights. The height of the smaller prism is one half that of the larger.

2 Octagonal Prisms

Illustration of 2 right octagonal prisms with congruent bases, but different heights. The height of…

Illustration of 2 Similar right octagonal prisms. The height and length of the edges of the smaller prism are one half that of the larger.

2 Similar Octagonal Prisms

Illustration of 2 Similar right octagonal prisms. The height and length of the edges of the smaller…