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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 torch.

Torch

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 torch.

Torch

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 torch.

Torch

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 torch.

Torch

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 torch.

Torch

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 torch.

Torch

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 torch.

Torch

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

"Tourmaline crystals show the forms of the Rhombohedral Class but with hemispherical development. They are also commonly characterized by the presence of three faces of a triangular prism." — Ford, 1912

Tourmaline

"Tourmaline crystals show the forms of the Rhombohedral Class but with hemispherical development. They…

"Tourmaline crystals show the forms of the Rhombohedral Class but with hemispherical development. They are also commonly characterized by the presence of three faces of a triangular prism." — Ford, 1912

Tourmaline

"Tourmaline crystals show the forms of the Rhombohedral Class but with hemispherical development. They…

"Tourmaline crystals show the forms of the Rhombohedral Class but with hemispherical development. They are also commonly characterized by the presence of three faces of a triangular prism." — Ford, 1912

Tourmaline

"Tourmaline crystals show the forms of the Rhombohedral Class but with hemispherical development. They…

"Hexagonal-rhombohedral; hemimorphic. Crystals usually prismatic, vertically striated. A triangular prism, with three faces, prominent, which with the tendency of the prism faces to be vertically striated and to round into each other gives the crystals usually a cross section like a spherical triangle." — Ford, 1912

Tourmaline

"Hexagonal-rhombohedral; hemimorphic. Crystals usually prismatic, vertically striated. A triangular…

"Hexagonal-rhombohedral; hemimorphic. Crystals usually prismatic, vertically striated. A triangular prism, with three faces, prominent, which with the tendency of the prism faces to be vertically striated and to round into each other gives the crystals usually a cross section like a spherical triangle. Crystals are commonly terminated by base and low positive and negative rhombohedrons; sometimes scalenohedrons are present. When the crystals are doubly terminated they usually show different forms at the opposite ends of the vertical axis." — Ford, 1912

Tourmaline

"Hexagonal-rhombohedral; hemimorphic. Crystals usually prismatic, vertically striated. A triangular…

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 of two straight lines cut by a transversal. The 8 angles formed are labeled.

2 Lines Cut By A Transversal

Illustration of two straight lines cut by a transversal. The 8 angles formed are labeled.

Illustration of two straight lines, m and n, cut by a transversal t.

2 Lines Cut By A Transversal

Illustration of two straight lines, m and n, cut by a transversal t.

Illustration of two straight lines, AB and CD, cut by a transversal EF.

2 Lines Cut By A Transversal

Illustration of two straight lines, AB and CD, cut by a transversal EF.

"The trapezohedron is a form composed of twenty-four trapezium-shaped faces, each of which intersects one of the crystallographic axes at unity and the other two at equal multiples." — Ford, 1912

Trapezohedron

"The trapezohedron is a form composed of twenty-four trapezium-shaped faces, each of which intersects…

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…

An illustration of a trapezoid with 4 sides and height labeled.

Trapezoid With Labels

An illustration of a trapezoid with 4 sides and height labeled.

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 tree.

Tree

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 tree.

Tree

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 tree.

Tree

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 tree.

Tree

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

A twenty-four sided geometric shape.

Triakisoctahedron

A twenty-four sided geometric shape.

An illustration of a triangle comprised of a church and two lines. This illustration can be used to determine the height of the church steeple, the hypotenuse, and distance of the tower from object one and two.

Triangle with Church

An illustration of a triangle comprised of a church and two lines. This illustration can be used to…

An illustration of a three triangles created with boats and a lighthouse. This is an example illustration used to fine the height of an object situated about the plane of observation, and its height above the plane.

Triangle with Lighthouse

An illustration of a three triangles created with boats and a lighthouse. This is an example illustration…

An illustration of a triangle comprised of a tower and two lines. This illustration can be used to determine the height of the tower, the hypotenuse, and distance of the tower from the object.

Triangle with Tower

An illustration of a triangle comprised of a tower and two lines. This illustration can be used to determine…

An illustration of a triangle comprised of a tree and two lines. This is an example of a problem that can be used to fine the distance of an inaccessible object without measuring elevation and whether on a horizontal plane or not.

Triangle with Tree

An illustration of a triangle comprised of a tree and two lines. This is an example of a problem that…

Illustration showing a triangle with angles A, B, and C labeled.

Triangle ABC

Illustration showing a triangle with angles A, B, and C labeled.

Illustration showing an acute triangle (one that has all three angles that are acute).

Acute Triangle

Illustration showing an acute triangle (one that has all three angles that are acute).

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 of a triangle showing that when a line parallel to the base of a triangle bisects one side, it bisects the other side also.

Triangle With Bisector Parallel to the Base

Illustration of a triangle showing that when a line parallel to the base of a triangle bisects one side,…

An illustration showing a circle with radius r inscribed in a triangle with sides a, b, and c.

Circle Inscribed In A Triangle

An illustration showing a circle with radius r inscribed in a triangle with sides a, b, and c.

An illustration showing a circle with sectors D and E inscribed in a triangle with angles, A, B, and C.

Circle Inscribed In A Triangle

An illustration showing a circle with sectors D and E inscribed in a triangle with angles, A, B, and…

Illustration used to circumscribe a circle about a given triangle.

Construction Used to Circumscribe a Circle About a Triangle

Illustration used to circumscribe a circle about a given triangle.

Illustration used to escribe a circle to a given triangle. "A circle which is tangent to one side of a triangle and to the the other two sides prolonged is said to be escribed to the triangle."

Construction Used to Escribe a Circle to a Triangle

Illustration used to escribe a circle to a given triangle. "A circle which is tangent to one side of…

Illustration used to inscribe a circle in a given triangle.

Construction Used to Inscribe a Circle in a Triangle

Illustration used to inscribe a circle in a given triangle.

Illustration showing an equiangular triangle (one that has all three angles that are equal).

Equiangular Triangle

Illustration showing an equiangular triangle (one that has all three angles that are equal).

"Having equal sides." — Williams, 1889

Equilateral triangle

"Having equal sides." — Williams, 1889

Illustration showing an equilateral triangle (one that has three sides equal).

Equilateral Triangle

Illustration showing an equilateral triangle (one that has three sides equal).

An illustration showing a triangle with interior angles A, B, C, and exterior angles D, and A' + B'.

Exterior And Interior Angles Of A Triangle

An illustration showing a triangle with interior angles A, B, C, and exterior angles D, and A' + B'.

Illustration showing a triangle with exterior angles. This can be used to show the sum of the three angles of a triangle is equal to two right angles.

Triangle with Exterior Angles Drawn

Illustration showing a triangle with exterior angles. This can be used to show the sum of the three…

Illustration showing an isosceles triangle (one that has two sides equal).

Isosceles Triangle

Illustration showing an isosceles triangle (one that has two sides equal).

Illustration showing an isosceles triangle with a segment inside. This can be used to show that in an isosceles triangle the angles opposite the equal sides are equal.

Isosceles Triangle With Interior Segment Drawn

Illustration showing an isosceles triangle with a segment inside. This can be used to show that in an…

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…

Illustration showing an obtuse triangle (one that has one obtuse angle).

Obtuse Triangle

Illustration showing an obtuse triangle (one that has one obtuse angle).

Illustration used to show the various parts of a triangle: sides, angles, medians, altitudes, bisectors, and segments.

Parts Of A Triangle

Illustration used to show the various parts of a triangle: sides, angles, medians, altitudes, bisectors,…

Illustration showing a perpendicular bisector of a triangle extended outside of the triangle.

Triangle With Perpendicular Bisector

Illustration showing a perpendicular bisector of a triangle extended outside of the triangle.

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

Perpendicular Bisectors In A Triangle

Illustration used to prove "The perpendicular bisectors of the sides of a triangle are concurrent in…

Illustration showing a right triangle (one that has one right angle).

Right Triangle

Illustration showing a right triangle (one that has one right angle).

Illustration showing a scalene triangle (one that has no two sides equal).

Scalene Triangle

Illustration showing a scalene triangle (one that has no two sides equal).

Illustration showing a triangle with an exterior segment drawn to show and exterior angle. This can be shown to show adjacent angles ACB and ACD as well.

Triangle With Segment Extended for Exterior Angle

Illustration showing a triangle with an exterior segment drawn to show and exterior angle. This can…

Illustration showing a triangle with an interior segment drawn

Triangle With Interior Segment

Illustration showing a triangle with an interior segment drawn

Illustration of a triangle with interior segments and angles labeled.

Segments and Angles in a Triangle

Illustration of a triangle with interior segments and angles labeled.

Illustration of a triangle with interior segments and angles labeled.

Segments and Angles in a Triangle

Illustration of a triangle with interior segments and angles labeled.

Illustration of triangle ABC with BE extended through the triangle at point D. Segment AB is equal to segment BD.

Segments Labeled In A Triangle

Illustration of triangle ABC with BE extended through the triangle at point D. Segment AB is equal to…

Illustration showing a triangle with a segment inside.

Triangle With Interior Segment Drawn

Illustration showing a triangle with a segment inside.

Illustration of three isosceles triangles with the same base AC but varying heights (as B gets farther from the base).

3 Isosceles Triangles Wit Equal Bases

Illustration of three isosceles triangles with the same base AC but varying heights (as B gets farther…