An instrument for making a reduced, enlarged, or exact copy of a plane figure

Pantograph

An instrument for making a reduced, enlarged, or exact copy of a plane figure

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 parallelogram.

Parallelogram

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 parallelogram.

Parallelogram

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 parallelogram.

Parallelogram

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 parallelogram.

Parallelogram

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 parrot fish.

Parrot Fish

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 parrot fish.

Parrot Fish

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 parrot fish.

Parrot Fish

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 parrot fish.

Parrot Fish

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

One large triangle for pattern block set.

Large Triangle for Pattern Block Set

One large triangle for pattern block set.

Six large triangles for pattern block set.

Large Triangles for Pattern Block Set

Six large triangles for pattern block set.

Six large triangles for pattern block set.

Large Triangles for Pattern Block Set

Six large triangles for pattern block set.

Nine large triangles for pattern block set.

Large Triangles for Pattern Block Set

Nine large triangles for pattern block set.

Forty-two small triangles for pattern block set.

Small Triangles for Pattern Block Set

Forty-two small triangles for pattern block set.

Pentagon with dimensions labeled. Pentagon can be used to calculate area by calculating individual triangles and finding the sum of the areas.

Pentagon With Triangular Sections For Area

Pentagon with dimensions labeled. Pentagon can be used to calculate area by calculating individual triangles…

"Argent, a pile, purpure. PILE. An angular figure like a wedge, formed by lines running from the dexter and sinister chief to the middle base." -Hall, 1862

Pile

"Argent, a pile, purpure. PILE. An angular figure like a wedge, formed by lines running from the dexter…

A circle with part of a triangle inscribed in it. They are lying on a coordinate plane.

Coordinate Plane

A circle with part of a triangle inscribed in it. They are lying on a coordinate plane.

Polygon consisting of 3 sides

3-sided Polygon

Polygon consisting of 3 sides

1/3 of a 3 sided polygon

Fractions of 3-sided Polygon

1/3 of a 3 sided polygon

2/3 of a 3 sided polygon

Fractions of 3-sided Polygon

2/3 of a 3 sided polygon

3/3 of a 3 sided polygon

Fractions of 3-sided Polygon

3/3 of a 3 sided polygon

3/3 of a 3 sided polygon with one piece detached

Fractions of 3-sided Polygon

3/3 of a 3 sided polygon with one piece detached

Triangle, triangular polygon

Triangular Polygon

Triangle, triangular polygon

Illustration of a pentagonal polyhedron that is formed by having two parallel congruent pentagonal bases connected by an alternating band of triangles and trapezoids, unlike an antiprism that has an alternating band of only triangles.

Polyhedron With Pentagon Bases

Illustration of a pentagonal polyhedron that is formed by having two parallel congruent pentagonal bases…

Illustration of a pentagonal polyhedron that is formed by having two parallel congruent pentagonal bases connected by an alternating band of triangles and trapezoids, unlike an antiprism that has an alternating band of only triangles.

Polyhedron With Pentagon Bases

Illustration of a pentagonal polyhedron that is formed by having two parallel congruent pentagonal bases…

Illustration of a pentagonal polyhedron that is formed by having two parallel congruent pentagonal bases connected by an alternating band of triangles and trapezoids, unlike an antiprism that has an alternating band of only triangles.

Polyhedron With Pentagon Bases

Illustration of a pentagonal polyhedron that is formed by having two parallel congruent pentagonal bases…

An illustration to exercise a stretched out, or development, image of the triangular prism using 4" by 5 " surface.

Triangular Prism Development Exercise

An illustration to exercise a stretched out, or development, image of the triangular prism using 4"…

An illustration to draw triangle prism's development, or stretched out surfaces, in a 4" by 5" surface.

Triangle Prism Exercise

An illustration to draw triangle prism's development, or stretched out surfaces, in a 4" by 5" surface.

Prism with triangular bases.

Right Triangular Prism

Prism with triangular bases.

A triangular prism.

Triangular prism

A triangular prism.

Illustration of a triangular prism - a prism whose base is a triangle.

Triangular Prism

Illustration of a triangular prism - a prism whose base is a triangle.

Illustration of a triangular prism; a prism whose bases are triangles.

Triangular Prism

Illustration of a triangular prism; a prism whose bases are triangles.

An illustration of a prismatoid with triangular faces and points labeled.

Prismatoid With Triangular Faces

An illustration of a prismatoid with triangular faces and points labeled.

Illustration to show that an angle bisector of a triangle divides the opposite side into segments which are proportional to the adjacent sides.

Angle Bisector of Triangle Dividing Opposite Side Into Proportionate Segments

Illustration to show that an angle bisector of a triangle divides the opposite side into segments which…

Illustration to show that a bisector of a an exterior angle of a triangle divides the opposite side into segments which are proportional to the adjacent sides.

Exterior Angle Bisector of Triangle Dividing Opposite Side Into Proportionate Segments

Illustration to show that a bisector of a an exterior angle of a triangle divides the opposite side…

Illustration to show that if a line is drawn through two sides of a triangle parallel to the third side, it divides those sides proportionally.

Triangle Divided by Parallel Lines to Form Proportionate Triangles

Illustration to show that if a line is drawn through two sides of a triangle parallel to the third side,…

Illustration to show that if a line divides two sides of a triangle proportionally, it is parallel to the third side.

Triangle Divided by Parallel Lines to Form Proportionate Triangles

Illustration to show that if a line divides two sides of a triangle proportionally, it is parallel to…

"If a pyramid be cut by a plane, parallel to the base, so as to form two parts, the lower part is called the frustum of the pyramid." — Hallock, 1905

Pyramid

"If a pyramid be cut by a plane, parallel to the base, so as to form two parts, the lower part is called…

Illustration of a right decagonal pyramid. The base is a decagon and the faces are isosceles triangles. The hidden edges are shown in this illustration.

Decagonal Pyramid

Illustration of a right decagonal pyramid. The base is a decagon and the faces are isosceles triangles.…

A sample exercise problem in completing the top part of the hexagonal pyramid and to create a development, or stretched out, of the image by creating edges at equal lengths, and revolving the sides.

Development Exercise of Hexagonal Pyramid

A sample exercise problem in completing the top part of the hexagonal pyramid and to create a development,…

A pentagonal pyramid problem exercise to complete the top view of the image, and development, or rolled out image, of the pyramid.

Development Exercise of Pentagonal Pyramid

A pentagonal pyramid problem exercise to complete the top view of the image, and development, or rolled…

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part is called a frustum. This frustum has triangular bases with 14 inch sides. The other sides are 16 and 22 inches. The altitude is 24 inches.

Pyramid Frustum With Triangular Bases and Height of 27 inches

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part…

Illustration of a right hexagonal pyramid with hidden edges shown. The base is a hexagon and the faces are isosceles triangles.

Hexagonal Pyramid

Illustration of a right hexagonal pyramid with hidden edges shown. The base is a hexagon and the faces…

Illustration of a right hexagonal pyramid with hidden edges shown.  The base is a hexagon and the faces are isosceles triangles.

Hexagonal Pyramid

Illustration of a right hexagonal pyramid with hidden edges shown. The base is a hexagon and the faces…

Illustration of a hollow right decagonal pyramid. The base is a decagon and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top.

Inverted Decagonal Pyramid

Illustration of a hollow right decagonal pyramid. The base is a decagon and the faces are isosceles…

Illustration of a hollow right hexagonal pyramid. The base is a hexagon and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top.

Inverted Hexagonal Pyramid

Illustration of a hollow right hexagonal pyramid. The base is a hexagon and the faces are isosceles…

Illustration of a hollow right nonagonal pyramid. The base is a nonagon and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top.

Inverted Nonagonal Pyramid

Illustration of a hollow right nonagonal pyramid. The base is a nonagon and the faces are isosceles…

Illustration of a hollow right octagonal pyramid. The base is an octagon and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top.

Inverted Octagonal Pyramid

Illustration of a hollow right octagonal pyramid. The base is an octagon and the faces are isosceles…

Illustration of a hollow right rectangular pyramid. The base is a rectangle and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top.

Inverted Rectangular Pyramid

Illustration of a hollow right rectangular pyramid. The base is a rectangle and the faces are isosceles…

Illustration of a hollow right heptagonal (septagonal) pyramid. The base is a heptagon and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top.

Inverted Septagonal/Heptagonal Pyramid

Illustration of a hollow right heptagonal (septagonal) pyramid. The base is a heptagon and the faces…

Illustration of a hollow right heptagonal (septagonal) pyramid. The base is a heptagon and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top. The hidden edges are shown in this drawing.

Inverted Septagonal/Heptagonal Pyramid

Illustration of a hollow right heptagonal (septagonal) pyramid. The base is a heptagon and the faces…

Illustration of a right nonagonal pyramid with hidden edges shown.  The base is a nonagon and the faces are isosceles triangles.

Nonagonal Pyramid

Illustration of a right nonagonal pyramid with hidden edges shown. The base is a nonagon and the faces…

Illustration of a right octagonal pyramid with hidden edges shown. The base is an octagon and the faces are isosceles triangles.

Octagonal Pyramid

Illustration of a right octagonal pyramid with hidden edges shown. The base is an octagon and the faces…

Illustration of a right pentagonal pyramid with hidden edges shown. The base is an pentagon and the faces are isosceles triangles.

Pentagonal Pyramid

Illustration of a right pentagonal pyramid with hidden edges shown. The base is an pentagon and the…

Illustration of a right pentagonal pyramid with hidden edges shown. The base is an pentagon and the faces are isosceles triangles.

Pentagonal Pyramid

Illustration of a right pentagonal pyramid with hidden edges shown. The base is an pentagon and the…

Illustration of a right pentagonal pyramid viewed from below with hidden edges shown. The base is an pentagon and the faces are isosceles triangles.

Pentagonal Pyramid

Illustration of a right pentagonal pyramid viewed from below with hidden edges shown. The base is an…

Illustration of a right pentagonal pyramid viewed from below. The base is an pentagon and the faces are isosceles triangles.

Pentagonal Pyramid

Illustration of a right pentagonal pyramid viewed from below. The base is an pentagon and the faces…

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the faces are isosceles triangles.

Rectangular Pyramid

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the…

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the faces are isosceles triangles. The height of the pyramid is much larger then the length and width of the base.

Rectangular Pyramid

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the…

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the faces are isosceles triangles.

Rectangular Pyramid

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the…