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Illustration showing two equal triangles.

Equal Triangles

Illustration showing two equal triangles.

Illustration showing two equal triangles. This can be used to show that two triangles are equal if the three sides of the one are equal, respectively, to the three sides of the other.

Equal Triangles by Side Side Side

Illustration showing two equal triangles. This can be used to show that two triangles are equal if the…

Illustration showing two equal right triangles. This can be used to show that two right triangles are equal if a leg and the hypotenuse of the one are equal, respectively, to a leg and the hypotenuse of the other.

Equal Right Triangles by Hypotenuse Leg

Illustration showing two equal right triangles. This can be used to show that two right triangles are…

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 showing three triangles. This is used to show the following theorem: If two triangles have two sides of the one equal, respectively, to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Three Triangles Used to Compare Sides

Illustration showing three triangles. This is used to show the following theorem: If two triangles have…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a triangular double arch.

Triangular Double Arch

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a triangular double arch.

Triangular Double Arch

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a triangular double arch.

Triangular Double Arch

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a triangular double arch.

Triangular Double Arch

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

"The trisoctahedron is a form composed of twenty-four isosceles triangular faces, each of which intersects two of the crystallographic axes at unity and the third axis at some multiple. There are various trisoctahedrons the faces of which have different inclinations." — Ford, 1912

Trisoctahedron

"The trisoctahedron is a form composed of twenty-four isosceles triangular faces, each of which intersects…

"The faces of the tristetrahedron correspond to one-half the faces of a trapezohedron." — Ford, 1912

Tristetrahedron

"The faces of the tristetrahedron correspond to one-half the faces of a trapezohedron." — Ford,…

An illustration showing how to construct two circles that tangent themselves and two given lines. "Draw the center line AB between the given lines; assume D to be the tangenting point of the circles; draw DC at right angles to AB. With C as center and CD as radius, draw the circle EDF. From E, draw Em at right angles to EF; and from F draw Fm at right angles to FE; then m and n are the centers for the required circles."

Construction Of Two Circles That Tangent Themselves and 2 Given Lines

An illustration showing how to construct two circles that tangent themselves and two given lines. "Draw…

"The cone B would be developed by cutting a right section as S—S whose stretchout will be a circle are, location the elements on it and finding the true length of each from the vertex to the line of intersection." —French, 1911

Intersection of Two Cones

"The cone B would be developed by cutting a right section as S—S whose stretchout will be a circle…

"If the cylinder A were to be developed a right section as at S—S would have to be taken, whose stretchout would be a straight line. If the cutting planes were taken at uniform distances apart, or at random, the elements would not be spaced uniformly on the stretchout but would be found as they project on the turned section of S—S." —French, 1911

Two Cylinders with Axes Not Intersecting

"If the cylinder A were to be developed a right section as at S—S would have to be taken, whose…

"The intersection of two cylinders might represent a dome on a boiler. If the top view of cylinder A is divided into a number of equal parts the points will represent the top views of elements."—French, 1911

Intersection of Two Cylinders

"The intersection of two cylinders might represent a dome on a boiler. If the top view of cylinder A…

Illustration of a vertical line segment. A line segment is a section of a line with definite endpoints.

Segment, Vertical Line

Illustration of a vertical line segment. A line segment is a section of a line with definite endpoints.

Illustration of a vertical line segment. A line segment is a section of a line with definite endpoints. The endpoints are A and B.

Segment, Vertical Line

Illustration of a vertical line segment. A line segment is a section of a line with definite endpoints.…

Vesuvianite.

Vesuvianite

Vesuvianite.

Vesuvianite

Vesuvianite

Vesuvianite

"Tetragonal. Prismatic in habit. Often vertically striated. Common forms are prisms of first and second orders, pyramid of first order and base." — Ford, 1912

Vesuvianite

"Tetragonal. Prismatic in habit. Often vertically striated. Common forms are prisms of first and second…

"Tetragonal. Prismatic in habit. Often vertically striated. Common forms are prisms of first and second orders, pyramid of first order and base." — Ford, 1912

Vesuvianite

"Tetragonal. Prismatic in habit. Often vertically striated. Common forms are prisms of first and second…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a vulture.

Vulture

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a vulture.

Vulture

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a vulture.

Vulture

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a vulture.

Vulture

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a water skier.

Water Skier

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a water skier.

Water Skier

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a water skier.

Water Skier

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a water skier.

Water Skier

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

"Tetragonal; tripyramidal. Crystals usually prismatic. Prominent forms are prisms of the first and second order, pyramid of first." — Ford, 1912

Wernerite

"Tetragonal; tripyramidal. Crystals usually prismatic. Prominent forms are prisms of the first and second…

"Tetragonal; tripyramidal. Crystals usually prismatic. Prominent forms are prisms of the first and second order, pyramid of first. Rarely shows the faces of the pyramid of the third order." — Ford, 1912

Wernerite

"Tetragonal; tripyramidal. Crystals usually prismatic. Prominent forms are prisms of the first and second…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a woman kneeling.

Woman Kneeling

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a woman kneeling.

Woman Kneeling

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a woman kneeling.

Woman Kneeling

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a woman kneeling.

Woman Kneeling.

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a woman standing.

Woman Standing

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a woman standing.

Woman Standing

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a woman standing.

Woman Standing

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a woman standing.

Woman Standing

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a yacht.

Yacht

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a yacht.

Yacht

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a yacht.

Yacht

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a yacht.

Yacht

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

"A crystal of zincite with a prism terminated by a pyramid above a basal pinacoid below." — Ford, 1912

Zincite

"A crystal of zincite with a prism terminated by a pyramid above a basal pinacoid below." — Ford,…

Zircon.

Zircon

Zircon.

Zircon.

Zircon

Zircon.

Zircon.

Zircon

Zircon.

Zircon.

Zircon

Zircon.

"Tetragonal. Crystals usually show a simple combination of prism and pyramid of the first order. The prism of the second order and a ditetragonal pyramid also at times observed." — Ford, 1912

Zircon

"Tetragonal. Crystals usually show a simple combination of prism and pyramid of the first order. The…