Axes showing trigonometric angles, and quadrants.

Trigonometric Angles and Quadrants

Axes showing trigonometric angles, and quadrants.

Trigonometric angle -229 degrees.

-229 Degree Trigonometric Angle

Trigonometric angle -229 degrees.

Trigonometric angle 467 degrees.

467 Degree Trigonometric Angle

Trigonometric angle 467 degrees.

Illustration to show that if through any point in the bisector of an angle a line is drawn parallel to either of the sides of the angle, the triangle thus formed is isosceles.

Angle Bisector Drawn Parallel to A Side

Illustration to show that if through any point in the bisector of an angle a line is drawn parallel…

Negative trigonometric angle with initial and terminal sides labeled.

Negative Trigonometric Angle

Negative trigonometric angle with initial and terminal sides labeled.

Positive trigonometric angle with initial and terminal sides labeled.

Positive Trigonometric Angle

Positive trigonometric angle with initial and terminal sides labeled.

Illustration showing that the bisector of a given angle is the locus of points equidistant from the sides of the angle.

Angle Bisector

Illustration showing that the bisector of a given angle is the locus of points equidistant from the…

Illustration showing that the perpendicular bisector of a given line is the locus of points equidistant from the extremities of the line.

Perpendicular Bisector of a Line

Illustration showing that the perpendicular bisector of a given line is the locus of points equidistant…

An illustration of a composite figure made up of a quadrilateral frustum and half of a cylinder. Frustum edges range between 6 feet and 11 feet 5 inches and cylinder has a height of 12 feet.

Composite Figure of Quadrilateral Frustum With Half of a Cylinder Attached

An illustration of a composite figure made up of a quadrilateral frustum and half of a cylinder. Frustum…

An illustration of both sides of a U.S. Dime.

Both sides of a Dime

An illustration of both sides of a U.S. Dime.

An illustration of both sides of a U.S. Dime that can be cutout and folded.

Two Sided Dime

An illustration of both sides of a U.S. Dime that can be cutout and folded.

"A polygon of...twelve sides is [a] dodecagon." —Hallock 1905

Dodecagon

"A polygon of...twelve sides is [a] dodecagon." —Hallock 1905

An illustration of both sides of a U.S. Dollar Coin.

Both sides of a Dollar

An illustration of both sides of a U.S. Dollar Coin.

An illustration of both sides of a U.S. Dollar Coin that can be cutout and folded.

Two Sided Dollar

An illustration of both sides of a U.S. Dollar Coin that can be cutout and folded.

Illustration used to show how to draw an equilateral triangle when given one side.

Construction Of Equilateral Triangle

Illustration used to show how to draw an equilateral triangle when given one side.

Illustration used to show how to draw an equilateral triangle when given the altitude.

Construction Of Equilateral Triangle

Illustration used to show how to draw an equilateral triangle when given the altitude.

A young girl standing with her arms at her sides.

Girl Standing

A young girl standing with her arms at her sides.

An illustration of both sides of a U.S. Half Dollar.

Both sides of a Half Dollar

An illustration of both sides of a U.S. Half Dollar.

An illustration of both sides of a U.S. Half Dollar that can be cutout and folded.

Two Sided Half Dollar

An illustration of both sides of a U.S. Half Dollar that can be cutout and folded.

"A polygon of...seven sides [is] a heptagon." —Hallock 1905

Heptagon

"A polygon of...seven sides [is] a heptagon." —Hallock 1905

"A polygon of...six sides a [is] a hexagon." —Hallock 1905

Hexagon

"A polygon of...six sides a [is] a hexagon." —Hallock 1905

An illustration of both sides of a U.S. Nickle.

Both sides of a Nickel

An illustration of both sides of a U.S. Nickle.

An illustration of both sides of a U.S. Nickle that can be cutout and folded.

Two Sided Nickel

An illustration of both sides of a U.S. Nickle that can be cutout and folded.

"A polygon of...eight sides [is] an octagon." —Hallock 1905

Octagon

"A polygon of...eight sides [is] an octagon." —Hallock 1905

An octahedron, or double four-sided pyramid. It has 8 sides.

Octahedron

An octahedron, or double four-sided pyramid. It has 8 sides.

An illustration of both sides of a U.S. Penny.

Both sides of a Penny

An illustration of both sides of a U.S. Penny.

An illustration of both sides of a U.S. Penny that can be cutout and folded.

Two Sided Penny

An illustration of both sides of a U.S. Penny that can be cutout and folded.

Illustration that shows similar polygons (pentagons) that can be used to show proportionality.

Similar Polygons (Pentagons) That Can Be Used To Show Proportionality

Illustration that shows similar polygons (pentagons) that can be used to show proportionality.

Illustration that shows similar polygons (pentagons) that can be used to show proportionality.

Similar Polygons (Pentagons) That Can Be Used To Show Proportionality

Illustration that shows similar polygons (pentagons) that can be used to show proportionality.

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 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…

An illustration of both sides of a U.S. Quarter.

Both sides of a Quarter

An illustration of both sides of a U.S. Quarter.

An illustration of both sides of a U.S. Quarter that can be cutout and folded.

Two Sided Quarter

An illustration of both sides of a U.S. Quarter that can be cutout and folded.

An illustration of a rectangle with lengths a and b and area ab.

Rectangle with Lengths a and b with Area ab

An illustration of a rectangle with lengths a and b and area ab.

An illustration of composite rectangle with lengths a, b, and c with area ac + bc. This illustration represents the product of c(a+b).

Rectangle with Lengths a, b, and c with Areas ac and bc

An illustration of composite rectangle with lengths a, b, and c with area ac + bc. This illustration…

A rectangular prism with labeled sides: AAAA are the four vertical parallel corners. BBBB and CCCC are the horizontal parallel edges.

Rectangular Prism

A rectangular prism with labeled sides: AAAA are the four vertical parallel corners. BBBB and CCCC are…

A geometric shape containing twelve faces.

Rhombic Dodecahedron

A geometric shape containing twelve faces.

Sawhorse used to length of legs.

Sawhorse

Sawhorse used to length of legs.

Diagram used to prove the theorem: "In a spherical triangle, the greater side is opposite the greater angle, and conversely."

Side Comparison of Spherical Triangle

Diagram used to prove the theorem: "In a spherical triangle, the greater side is opposite the greater…

An illustration of a hollow square (square within square) with outer square having a side of 2s+6 and inner square having a side of s-2. Illustration could be used for calculating area.

Hollow Square with Dimensions of 2s+6 and s-2

An illustration of a hollow square (square within square) with outer square having a side of 2s+6 and…

Two set squares, whose sides are 3,4, and 5 in., are placed so that their 4-in. sides and right angles coincide, and the angle between the 3-in. sides is 50 degrees. Theta, Ǝ is the angle between the longest sides.

Two Squares With Sides of Lengths 3,4,5 Placed at Right Angles to Each Other

Two set squares, whose sides are 3,4, and 5 in., are placed so that their 4-in. sides and right angles…

Illustration used to prove that "If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second."

2 Triangles Theorem

Illustration used to prove that "If two triangles have two sides of one equal respectively to two sides…

Illustration used to prove that "If two triangles have two sides of one equal respectively to two sides of the other, but the third side of the first greater than the third side of the second, then the angle opposite the third side of the first is greater than the angle opposite the third side of the second."

2 Triangles Theorem

Illustration used to prove that "If two triangles have two sides of one equal respectively to two sides…

Illustration used to prove that "If two sides of a triangle are unequal, the angle opposite the greater side is greater than the angle opposite the less side."

Sides of Triangle Theorem

Illustration used to prove that "If two sides of a triangle are unequal, the angle opposite the greater…

Illustration used to prove that "The sum of any two sides of a triangle is greater than the third side."

Sides of Triangle Theorem

Illustration used to prove that "The sum of any two sides of a triangle is greater than the third side."

Triangle with sides a, b, c and angles A, B, C labeled.

Triangle

Triangle with sides a, b, c and angles A, B, C labeled.

Triangle with sides labeled with numerals 28, 36, 40 and angles A, B, C labeled.

Triangle 28, 36, 40

Triangle with sides labeled with numerals 28, 36, 40 and angles A, B, C labeled.

Triangle with labels A, B, C, D

Triangle

Triangle with labels A, B, C, D

Illustration to show that if one of the legs of an isosceles triangle is produced through the vertex by its own length, the line joining he end of the leg produced to the nearer end of the base is perpendicular to the base.

Leg Produced through the Vertex of an Isosceles Triangle

Illustration to show that if one of the legs of an isosceles triangle is produced through the vertex…

Illustration to show that if the lines joining the middle points of the sides of a triangle divide the triangle into four equal triangles.

Midpoints of Triangle Divide Triangle into Four Equal Triangles

Illustration to show that if the lines joining the middle points of the sides of a triangle divide the…

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 to show the perpendiculars dropped from any point in the equilateral triangle to the three sides is constant, and equal to the altitude.

Perpendiculars Dropped Any Point in the Equilateral Triangle

Illustration to show the perpendiculars dropped from any point in the equilateral triangle to the three…

Right triangle with sides a, b, c and angles A, B, C labeled.

Right Triangle ABC

Right triangle with sides a, b, c and angles A, B, C labeled.

Illustration of a right triangle with legs labeled 150 and 85. This could be used to find the hypotenuse using Pythagorean Theorem.

Right Triangle With Sides 85 and 150

Illustration of a right triangle with legs labeled 150 and 85. This could be used to find the hypotenuse…

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 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 to show if two triangles have two sides of the one equal, respectively, to two sides of the other, and the angles opposite two equal sides equal, the angles opposite the other two equal sides are equal or supplementary, and if equal the triangles are equal.

Proof of Equal Triangles Drawing

Illustration to show if two triangles have two sides of the one equal, respectively, to two sides of…