Illustration of a regular nonagon inscribed in an equilateral triangle. This could also be described as an equilateral triangle circumscribed about a regular nonagon.

Nonagon Inscribed in a Triangle

Illustration of a regular nonagon inscribed in an equilateral triangle. This could also be described…

Illustration of oblique triangle used to find distance across a river.

Oblique Triangle for Distance Across a River

Illustration of oblique triangle used to find distance across a river.

Illustration of oblique triangle used to find distance across a river.

Oblique Triangle for Distance Across a River

Illustration of oblique triangle used to find distance across a river.

Illustration of oblique triangle used to find distance across a lake.

Oblique Triangle for Distance Across Lake

Illustration of oblique triangle used to find distance across a lake.

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

Obtuse Triangle

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

Obtuse triangle with altitude drawn.

Obtuse Triangle

Obtuse triangle with altitude drawn.

Obtuse triangle with altitude and one median drawn.

Obtuse Triangle

Obtuse triangle with altitude and one median drawn.

Triangle with sides a,b,c and height/altitude h.

Obtuse Triangle With Height Drawn

Triangle with sides a,b,c and height/altitude h.

Illustration to show altitudes in a triangle. It is known as the orthocenter.

Orthocenter of Triangle

Illustration to show altitudes in a triangle. It is known as the orthocenter.

Illustration of a triangle with a segment parallel to the base.

Triangle With Parallel Segment Drawn

Illustration of a triangle with a segment parallel to the base.

Illustration to show that if from any point in the base of an isosceles triangle parallels to the legs are drawn, a parallelogram is formed whose perimeter is constant, being equal to the sum of the legs of the triangle.

Isosceles Triangle With Parallelogram inside

Illustration to show that if from any point in the base of an isosceles triangle parallels to the legs…

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 to show the perpendiculars dropped from the midpoint of the base to the legs of an isosceles triangle are equal.

Perpendiculars Dropped From Midpoint of Base to Legs of Isosceles Triangles

Illustration to show the perpendiculars dropped from the midpoint of the base to the legs of an isosceles…

Illustration to show that the difference of the distances from any point in the base produced of an isosceles triangle to the equal sides of the triangle is constant.

Point in Base of Isosceles Triangle

Illustration to show that the difference of the distances from any point in the base produced of an…

Right triangle with squares that can be used to illustrate the Pythagorean Theorem.

Pythagorean Theorem Triangle

Right triangle with squares that can be used to illustrate the Pythagorean Theorem.

Right triangle with square

Right Triangle

Right triangle with square

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

Right Triangle

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

Illustration of a right triangle with the midpoint of the hypotenuse drawn.

Right Triangle With Midpoint of Hypotenuse Drawn

Illustration of a right triangle with the midpoint of the hypotenuse drawn.

Illustration of a right triangle with one angle the double of the other.

Right Triangle With One Angle Double the Other

Illustration of a right triangle with one angle the double of the other.

The Rondinella triangle is a modified triangle ruler, where the hypotenuse is outwardly bent.

Rondinella Triangle

The Rondinella triangle is a modified triangle ruler, where the hypotenuse is outwardly bent.

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 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…

Steam pipe illustration of 30-60-90 triangle.

Triangle Steam Pipe

Steam pipe illustration of 30-60-90 triangle.

Illustration showing a triangle with a segment inside.

Triangle With Interior Segment Drawn

Illustration showing a triangle with a segment inside.

The Zange triangle is a modified triangle ruler, where one of the legs is longer making the hypotenuse is elongated.

Zange Triangle

The Zange triangle is a modified triangle ruler, where one of the legs is longer making the hypotenuse…

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…

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.

"A circle may be considered as made up of triangles whose bases form the circumference, and whose altitude is the radius (1/2 diameter) of the circle." This is clearly shown by the cut at the left.

Circle Made Up Of Triangles

"A circle may be considered as made up of triangles whose bases form the circumference, and whose altitude…

Illustration showing two equal triangles.

Equal Triangles

Illustration showing two equal triangles.

Illustration used to show that two triangles are equal if the three sides of one are equal respectively to the three sides of the other.

Equal Triangles

Illustration used to show that two triangles are equal if the three sides of one are equal respectively…

Illustration showing two equal triangles. This can be used to show that two triangles are equal if the three sides of the one are equal, respectively, to the three sides of the other.

Equal Triangles by Side Side Side

Illustration showing two equal triangles. This can be used to show that two triangles are equal if the…

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…

An illustration showing an isosceles triangle in an equilateral triangle.

Equilateral And Isosceles Triangles

An illustration showing an isosceles triangle in an equilateral triangle.

Illustration of an equilateral triangle inscribed in an equilateral triangle. The smaller triangle is created by joining the midpoints of the sides of the larger triangle. The area of the inscribed triangle is 1/4 the area of the larger triangle.

Equilateral Triangle Inscribed In An Equilateral Triangle

Illustration of an equilateral triangle inscribed in an equilateral triangle. The smaller triangle is…

Illustration of an equilateral triangle inscribed in an equilateral triangle by joining the midpoints of the sides of the larger triangle. 3 smaller equilateral triangles are then constructed in the remaining area by joining the midpoints of the other 3 triangles.

Equilateral Triangles Inscribed In An Equilateral Triangle

Illustration of an equilateral triangle inscribed in an equilateral triangle by joining the midpoints…

Illustration of an equilateral triangle inscribed in an equilateral triangle by joining the midpoints of the sides of the larger triangle. Thus, there are 4 equilateral triangles inside of the large triangle. Inside each of the 4 smaller equilateral triangles another equilateral triangle is constructed by joining the midpoints of the sides.

Equilateral Triangles Inscribed In Equilateral Triangles

Illustration of an equilateral triangle inscribed in an equilateral triangle by joining the midpoints…

Illustration of an equilateral triangle inscribed in an equilateral triangle by joining the midpoints of the sides of the larger triangle. Inside the smaller equilateral triangle another inscribed equilateral triangle is constructed by joining the midpoints of the sides.

Equilateral Triangles Inscribed In Equilateral Triangles

Illustration of an equilateral triangle inscribed in an equilateral triangle by joining the midpoints…

The Kelsey triangle is a modified triangle ruler, where the hypotenuse is inwardly bent.

Kelsey Triangles

The Kelsey triangle is a modified triangle ruler, where the hypotenuse is inwardly bent.

Illustration of polar and spherical triangles.

Polar and Spherical Triangles

Illustration of polar and spherical triangles.

Illustration of polar triangles.

Polar Triangles in Sphere

Illustration of polar triangles.

Illustration showing two equal right triangles. This can be used to show that two right triangles are equal if a leg and the hypotenuse of the one are equal, respectively, to a leg and the hypotenuse of the other.

Equal Right Triangles by Hypotenuse Leg

Illustration showing two equal right triangles. This can be used to show that two right triangles are…

Illustration to show two triangles with the same base and on the same side of the base.

Triangles With The Same Base

Illustration to show two triangles with the same base and on the same side of the base.

Similar triangles with corresponding sides labeled.

Similar Triangles

Similar triangles with corresponding sides labeled.

Similar triangles with corresponding sides labeled.

Similar Triangles

Similar triangles with corresponding sides labeled.

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 2 similar triangles with altitudes drawn.

Similar triangles

Illustration of 2 similar triangles with altitudes drawn.

Illustration of two similar triangles, abc and ABC.

Similar Triangles

Illustration of two similar triangles, abc and ABC.

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 of similar triangles used to find distance across a lake.

Similar Triangles for Distance Across Lake

Illustration of similar triangles used to find distance across a lake.

Illustration of similar triangles used to find distance across a stream

Similar Triangles for Distance Across Stream

Illustration of similar triangles used to find distance across a stream

Illustration of similar triangles used to find height of smokestack.

Similar Triangles for Height of Smokestack

Illustration of similar triangles used to find height of smokestack.

Illustration that shows two similar triangles with altitudes drawn.

Similar Triangles With Altitudes Drawn

Illustration that shows two similar triangles with altitudes drawn.

Illustration of symmetrical spherical triangles.

Symmetric Spherical Triangles

Illustration of symmetrical spherical triangles.