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

Obtuse Triangle ABC

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

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.

An illustration of an obtuse triangle with the height/altitude labeled h.

Obtuse Triangle

An illustration of an obtuse triangle with the height/altitude labeled h.

Triangle ABC with sides a,b,c labeled and angles A,B,C labeled and h labeled as height.

Obtuse Triangle ABC With Height h

Triangle ABC with sides a,b,c labeled and angles A,B,C labeled and h labeled as height.

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 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 that the perpendicular bisector of the base of an isosceles triangle passes through the vertex and bisects the angle at the vertex.

Perpendicular Bisector of the Base of an Isosceles Triangle

Illustration to show that the perpendicular bisector of the base of an isosceles triangle passes through…

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…

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…

Trigonometric reference triangles/angles drawn for 60 degree reference angel in quadrants I and II.

Trigonometric Reference Triangles/Angles (60 degrees) Drawn in Quadrants

Trigonometric reference triangles/angles drawn for 60 degree reference angel in quadrants I and II.

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.

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

Right Triangle ABC

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

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

Right Triangle ABC

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

Right triangle ABC with sides m,n, p and angles A, B, C labeled.

Right Triangle ABC

Right triangle ABC with sides m,n, p and angles A, B, C labeled.

Right triangle ABC with angles A, B, C labeled.

Right Triangle ABC

Right triangle ABC with 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 used to show the Pythagorean Theorem (the square of the hypotenuse is equal to the sum of the squares of the legs).

Right Triangle

Illustration of a right triangle used to show the Pythagorean Theorem (the square of the hypotenuse…

Right triangle ABC with angles A, B, C labeled and leg of 13 with hypotenuse of 15.

Right Triangle with leg 13 and hypotenuse 15

Right triangle ABC with angles A, B, C labeled and leg of 13 with hypotenuse of 15.

Right triangle ABC with angles A, B, C labeled and sides of length 3,4, and 5

Right Triangle 3,4,5

Right triangle ABC with angles A, B, C labeled and sides of length 3,4, and 5

Right triangle ABC with angles A, B, C to be used for finding distance across a river. This is a trigonometry problem. Wishing to determine the width of the river, I observed a tree standing directly across on the bank. The angle of elevation of the top of the tree was 32 degrees. At 150 ft. back from this point and in the same direction from the tree the angle of elevation of the top of the tree was 21 degrees. Find the width of the river.

Right Triangle For Finding Distance Across a River

Right triangle ABC with angles A, B, C to be used for finding distance across a river. This is a trigonometry…

Inclined plane forming right triangle showing the velocity of a body sliding a distance,s, down a smooth horizontal plane.

Inclined Plane Forming Right Triangle

Inclined plane forming right triangle showing the velocity of a body sliding a distance,s, down a smooth…

Right triangle OCB that can be used to show the relationships between x, y, r, and Θ.

Right Triangle OCB With, x, y, and r shown

Right triangle OCB that can be used to show the relationships between x, y, r, and Θ.

Illustration of a right triangle that can be used to show Pythagorean theorem. "In any right triangle, the square described upon the hypotenuse is equal to the sum of the squares described upon the other two sides."

Right Triangle Showing Pythagorean Theorem

Illustration of a right triangle that can be used to show Pythagorean theorem. "In any right triangle,…

Right triangle OQP with angle of 35 degrees, height of .70 inches, and leg of 1 inch.

Right Triangle With Sides .7 and 1 and Angle of 35 degrees

Right triangle OQP with angle of 35 degrees, height of .70 inches, and leg of 1 inch.

Right triangle OQP with angle of 40 degrees, height of .64 inches, and hypotenuse of 1 inch.

Right Triangle With Sides .64 and 1 and Angle of 40 degrees

Right triangle OQP with angle of 40 degrees, height of .64 inches, and hypotenuse of 1 inch.

Right triangle ABC with a base angle of 67 degrees 4208 minutes and a hypotenuse of 23.47 ft.

Right Triangle ABC With Angle 67 degrees 42.8 minutes and Hypotenuse 23.47 ft.

Right triangle ABC with a base angle of 67 degrees 4208 minutes and a hypotenuse of 23.47 ft.

Right triangle ABC with a leg of 23.85 feet and a hypotenuse of 35.62 feet.

Right Triangle ABC With Leg 23.85 ft. and Hypotenuse 35.62 ft.

Right triangle ABC with a leg of 23.85 feet and a hypotenuse of 35.62 feet.

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.

Right triangle with side .024967 and hypotenuse .04792.

Right Triangle With Side .024967 and Hypotenuse .04792

Right triangle with side .024967 and hypotenuse .04792.

Right triangle with side 234 and hypotenuse 308.

Right Triangle With Side 234 and Hypotenuse 308

Right triangle with side 234 and hypotenuse 308.

Right triangle with sides 15 and 18.

Right Triangle With Sides 15 and 18

Right triangle with sides 15 and 18.

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…

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 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…

Special right triangle with angles 30 degrees, 60 degrees, and 90 degrees with side measures/relationships shown.

Special Right Triangle with Angles 30, 60, 90 degrees

Special right triangle with angles 30 degrees, 60 degrees, and 90 degrees with side measures/relationships…

Special right triangle with angles 45 degrees, 45 degrees, and 90 degrees with side measures/relationships shown.

Special Right Triangle with Angles 45, 45, 90 degrees

Special right triangle with angles 45 degrees, 45 degrees, and 90 degrees with side measures/relationships…

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…

Triangle ABC and triangle ABC'. This illustration could be used to demonstrate the law of sines.

Triangles ABC and ABC'

Triangle ABC and triangle ABC'. This illustration could be used to demonstrate the law of sines.

"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 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…

Equilateral triangles set up along a coordinate plane.

Equilateral Triangles

Equilateral triangles set up along a coordinate plane.

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.