Illustration of 3 equal dihedral angles. "Two dihedral angles have the same ratio as their plane angles."

Equal Dihedral Angles

Illustration of 3 equal dihedral angles. "Two dihedral angles have the same ratio as their plane angles."

"If from any point on the circumference of a circle, a perpendicular be let fall upon a given diameter, this perpendicular will be a mean proportional between the two parts into which it divides the diameter."

Circle With a Perpendicular Drawn to the Diameter

"If from any point on the circumference of a circle, a perpendicular be let fall upon a given diameter,…

Line divided into proportional parts.

Line Divided Into Parts

Line divided into proportional parts.

Illustration that shows if two parallel lines are cut by three or more transversals that pass through the same point, the corresponding segments are proportional.

Parallel Lines Cut by Transversals

Illustration that shows if two parallel lines are cut by three or more transversals that pass through…

Illustration that shows if two parallel lines are cut by three or more transversals that pass through the same point, the corresponding segments are proportional.

Parallel Lines Cut by Transversals

Illustration that shows if two parallel lines are cut by three or more transversals that pass through…

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 of 2 right octagonal prisms with congruent bases, but different heights. The height of the smaller prism is one half that of the larger.

2 Octagonal Prisms

Illustration of 2 right octagonal prisms with congruent bases, but different heights. The height of…

Illustration of 2 Similar right octagonal prisms. The height and length of the edges of the smaller prism are one half that of the larger.

2 Similar Octagonal Prisms

Illustration of 2 Similar right octagonal prisms. The height and length of the edges of the smaller…

Illustration of 2 similar right decagonal prisms. Both have regular decagons for bases and rectangular faces. The height of the prism and length of the side of the decagon on the smaller decagonal prism are one half that of the larger.

Similar Decagonal Prisms

Illustration of 2 similar right decagonal prisms. Both have regular decagons for bases and rectangular…

Illustration of 2 similar right heptagonal/septagonal prisms. Both have regular heptagons/septagons for bases and rectangular faces. The height of the prism and length of the side of the heptagon on the smaller heptagonal prism are one half that of the larger.

Similar Heptagonal/Septagonal Prisms

Illustration of 2 similar right heptagonal/septagonal prisms. Both have regular heptagons/septagons…

Illustration of 2 similar right hexagonal prisms. The height of the prism and length of the side of the hexagon on the smaller hexagonal prism are one half that of the larger.

Similar Hexagonal Prisms

Illustration of 2 similar right hexagonal prisms. The height of the prism and length of the side of…

Illustration of 2 similar right hexagonal prisms. The height of the prism and length of the side of the hexagon on the smaller hexagonal prism are one half that of the larger.

Similar Hexagonal Prisms

Illustration of 2 similar right hexagonal prisms. The height of the prism and length of the side of…

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 parallel lines are cut by any number of parallels, the corresponding intercepts are proportional.

Parallel Lines Cut by Parallels, Corresponding Intercepts Proportional

Illustration to show that if parallel lines are cut by any number of parallels, the corresponding intercepts…

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…

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 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 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…

Right triangle inscribed in semicircle. Illustration shows that the perpendicular from any point in the circumference to the diameter of a circle is the mean proportional between the segments of the diameter.

Right Triangle Inscribed in Semicircle Shows Mean Proportional

Right triangle inscribed in semicircle. Illustration shows that the perpendicular from any point in…

Illustration that shows two mutually equiangular triangles are similar.

Mutually Equiangular Similar Triangles

Illustration that shows two mutually equiangular triangles are similar.

Illustration that shows that two triangles which have their sides respectively parallel, or respectively perpendicular, are similar.

Similar Triangles With Respective Sides Parallel or Perpendicular

Illustration that shows that two triangles which have their sides respectively parallel, or respectively…

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 that shows two similar triangles with altitudes drawn.

Similar Triangles With Altitudes Drawn

Illustration that shows two similar triangles with altitudes drawn.