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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 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 2 similar right pentagonal pyramids with hidden edges shown. The height of the pyramid and length of the side of the pentagon (base) on the smaller pentagonal pyramid are one half that of the larger.

Similar Pentagonal Pyramids

Illustration of 2 similar right pentagonal pyramids with hidden edges shown. The height of the pyramid…

Illustration of 2 right pentagonal pyramids with hidden edges shown. The pentagonal bases are congruent, but the height of the smaller pyramid is one half that of the larger.

2 Right Pentagonal Pyramids

Illustration of 2 right pentagonal pyramids with hidden edges shown. The pentagonal bases are congruent,…

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 2 right rectangular pyramids with hidden edges shown. The rectangular bases are congruent, but the height of the smaller pyramid is one half that of the larger.

2 Right Rectangular Pyramids

Illustration of 2 right rectangular pyramids with hidden edges shown. The rectangular bases are congruent,…

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

Skewed Rectangular Pyramid

Illustration of a non-right, or skewed, rectangular pyramid with hidden edges shown. The base is a rectangle…

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 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 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 an equilateral triangle inscribed in a closed concave geometric figure with 24 sides in the shape of a 12-point star. The two figures are concentric.

Triangle Inscribed In A 12-Point Star

Illustration of an equilateral triangle inscribed in a closed concave geometric figure with 24 sides…

Illustration of an equilateral triangle inscribed in a circle. This can also be described as a circle circumscribed about an equilateral triangle.

Triangle Inscribed In A Circle

Illustration of an equilateral triangle inscribed in a circle. This can also be described as a circle…

Illustration of an equilateral triangle circumscribed about a circle. This can also be described as a circle inscribed in an equilateral triangle.

Triangle Circumscribed About A Circle

Illustration of an equilateral triangle circumscribed about a circle. This can also be described as…

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…

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are pentagons.

Pentagonal Antiprism

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are pentagons.

Pentagonal Antiprism

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a decagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are decagons.

Decagonal Antiprism

Illustration of a decagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a decagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are decagons.

Decagonal Antiprism

Illustration of a decagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a dodecagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are dodecagons.

Dodecagonal Antiprism

Illustration of a dodecagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a dodecagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are dodecagons.

Dodecagonal Antiprism

Illustration of a dodecagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a heptagonal, or sometimes known as a septagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are heptagons/septagons.

Heptagonal/Septagonal Antiprism

Illustration of a heptagonal, or sometimes known as a septagonal antiprism. An antiprism is formed by…

Illustration of a heptagonal, or sometimes known as a septagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are heptagons/septagons.

Heptagonal/Septagonal Antiprism

Illustration of a heptagonal, or sometimes known as a septagonal antiprism. An antiprism is formed by…

Illustration of a skewed (non-right) heptagonal, or sometimes known as a septagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are heptagons/septagons.

Skewed Heptagonal/Septagonal Antiprism

Illustration of a skewed (non-right) heptagonal, or sometimes known as a septagonal antiprism. An antiprism…

Illustration of a hexagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are hexagons.

Hexagonal Antiprism

Illustration of a hexagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a skewed (non-right) hexagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are hexagons.

Skewed Hexagonal Antiprism

Illustration of a skewed (non-right) hexagonal antiprism. An antiprism is formed by having two parallel…

Illustration of a hexagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are hexagons.

Hexagonal Antiprism

Illustration of a hexagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a nonagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are nonagons.

Nonagonal Antiprism

Illustration of a nonagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a skewed (non-right) nonagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are nonagons.

Skewed Nonagonal Antiprism

Illustration of a skewed (non-right) nonagonal antiprism. An antiprism is formed by having two parallel…

Illustration of a nonagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are nonagons.

Nonagonal Antiprism

Illustration of a nonagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of an octagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are octagons.

Octagonal Antiprism

Illustration of an octagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of an octagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are octagons.

Octagonal Antiprism

Illustration of an octagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a skewed (non-right) octagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are octagons.

Skewed Octagonal Antiprism

Illustration of a skewed (non-right) octagonal antiprism. An antiprism is formed by having two parallel…

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are pentagons.

Pentagonal Antiprism

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are pentagons.

Pentagonal Antiprism

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a skewed (non-right) pentagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are pentagons.

Skewed Pentagonal Antiprism

Illustration of a skewed (non-right) pentagonal antiprism. An antiprism is formed by having two parallel…

Illustration used to prove the Pythagorean Theorem, according to Euclid. A perpendicular is drawn from the top vertex of the right triangle extended through the bottom square, forming 2 rectangles. Each rectangle has the same area as one of the two legs. This proves that the sum of the squares of the legs is equal to the square of the hypotenuse (Pythagorean Theorem).

Euclid's Pythagorean Theorem Proof

Illustration used to prove the Pythagorean Theorem, according to Euclid. A perpendicular is drawn from…

Illustration that can be used to prove the Pythagorean Theorem, the sum of the squares of the legs is equal to the square of the hypotenuse.

Geometric Pythagorean Theorem Proof

Illustration that can be used to prove the Pythagorean Theorem, the sum of the squares of the legs is…

Illustration that can be used to prove the Pythagorean Theorem, the sum of the squares of the legs is equal to the square of the hypotenuse. The geometrical illustration depicts a 3,4,5 right triangle with the square units drawn to prove that the sum of the squares of the legs (9 + 16) equals the square of the hypotenuse.

Geometric Pythagorean Theorem Proof

Illustration that can be used to prove the Pythagorean Theorem, the sum of the squares of the legs is…

A visual illustration used to prove the Pythagorean Theorem by rearrangement. When the 4 identical triangles are removed, the areas are equal. Thus, proving the sum of the squares of the legs is equal to the square of the hypotenuse.

Pythagorean Theorem Proof by Rearrangement

A visual illustration used to prove the Pythagorean Theorem by rearrangement. When the 4 identical triangles…

Illustration of a 6-point star created by two equilateral triangles (often described as the Star of David) inscribed in a circle. This can also be described as a circle circumscribed about a 6-point star, or two triangles.

Star Inscribed In A Circle

Illustration of a 6-point star created by two equilateral triangles (often described as the Star of…

Illustration of a triangle with its incircle and three excircles constructed.

Triangle With Circle Constructions

Illustration of a triangle with its incircle and three excircles constructed.

Triangles are made of various substances such as wood, rubber, celluloid, and steel.

45 Degree Triangle

Triangles are made of various substances such as wood, rubber, celluloid, and steel.

Triangles are made of various substances such as wood, rubber, celluloid, and steel.

30-60 Degree Triangle

Triangles are made of various substances such as wood, rubber, celluloid, and steel.

A triangle and a T-square can be used in conjunction to draw a rectangle.

Drawing Rectangles

A triangle and a T-square can be used in conjunction to draw a rectangle.

The triangle scale has six surfaces for different graduations, and the scales are arranged so that the drawings may be made in any proportion to the actual size.

Triangle Scales

The triangle scale has six surfaces for different graduations, and the scales are arranged so that the…

Square pattern exercise: Divide A D and A B into 4 equal parts and draw horizontal and vertical lines. Now divide these dimensions, A L, M N, etc., and E F, G B, etc., into 4 equal parts- each 1/4 inch- and draw light pencil lines with the T-square and triangle.

Square Exercise

Square pattern exercise: Divide A D and A B into 4 equal parts and draw horizontal and vertical lines.…

Weave pattern exercise: Divide A D and A B into 8 equal parts, and through the points O, P, Q, H, I, J, etc., draw horizontal and vertical lines. Now draw lines connecting O and H, P and I, Q and J, etc. As these lines form an angle of 45 degrees with the horizontal, a 45-degree triangle may be used. Similarly from each one of the given points on A B and A D, draw lines at an angle of 45 degrees to B C and D C respectively.

Weave Exercise

Weave pattern exercise: Divide A D and A B into 8 equal parts, and through the points O, P, Q, H, I,…

Vertical lines are drawn by using a triangle held against the T-square.

Drawing a Vertical Line

Vertical lines are drawn by using a triangle held against the T-square.

15 degrees with the horizontal or 75 degrees with the vertical.

Triangle Set Up for 15 Degrees

15 degrees with the horizontal or 75 degrees with the vertical.

30 degrees with the horizontal or 60 degrees with the vertical.

Triangle Set Up for 30 Degrees

30 degrees with the horizontal or 60 degrees with the vertical.

45 degrees with the horizontal or 45 degrees with the vertical.

Triangle Set Up for 45 Degrees

45 degrees with the horizontal or 45 degrees with the vertical.

60 degrees with the horizontal or 30 degrees with the vertical.

Triangle Set Up for 60 Degrees

60 degrees with the horizontal or 30 degrees with the vertical.

75 degrees with the horizontal or 15 degrees with the vertical.

Triangle Set Up for 75 Degrees

75 degrees with the horizontal or 15 degrees with the vertical.

Parallel lines are drawn by using a triangle in combination with a T-square. To draw a line parallel to the one given, place a triangle against the T-square and move them together until the hypotenuse of the triangle matches the line. Hold the T-square firmly and slide the triangle in the direction of the arrow until the desired position of the parallel line is reached.

Drawing Parallel Lines Exercise

Parallel lines are drawn by using a triangle in combination with a T-square. To draw a line parallel…