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An isosceles triangle with angles 93, 43.5, 43.5

Isosceles Triangle degrees 93, 43.5, 43.5

An isosceles triangle with angles 93, 43.5, 43.5

An isosceles triangle with angles 94, 43, 43

Isosceles Triangle degrees 94, 43, 43

An isosceles triangle with angles 94, 43, 43

An isosceles triangle with angles 95, 42.5, 42.5

Isosceles Triangle degrees 95, 42.5, 42.5

An isosceles triangle with angles 95, 42.5, 42.5

An isosceles triangle with angles 96, 42, 42

Isosceles Triangle degrees 96, 42, 42

An isosceles triangle with angles 96, 42, 42

An isosceles triangle with angles 97, 41.5, 41.5

Isosceles Triangle degrees 97, 41.5, 41.5

An isosceles triangle with angles 97, 41.5, 41.5

An isosceles triangle with angles 98, 41, 41

Isosceles Triangle degrees 98, 41, 41

An isosceles triangle with angles 98, 41, 41

An isosceles triangle with angles 99, 40.5, 40.5

Isosceles Triangle degrees 99, 40.5, 40.5

An isosceles triangle with angles 99, 40.5, 40.5

Illustration showing an isosceles triangle with a segment inside. This can be used to show that in an isosceles triangle the angles opposite the equal sides are equal.

Isosceles Triangle With Interior Segment Drawn

Illustration showing an isosceles triangle with a segment inside. This can be used to show that in an…

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 the medians drawn to the legs of an isosceles triangle.

Medians Drawn Drawn to Legs of Isosceles Triangles

Illustration to show the medians drawn to the legs of an isosceles triangle.

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

Obtuse Triangle

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

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 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 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 used to prove "The perpendicular bisectors of the sides of a triangle are concurrent in a point which is equidistant from the three vertices of the triangle."

Perpendicular Bisectors In A Triangle

Illustration used to prove "The perpendicular bisectors of the sides of a triangle are concurrent in…

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…

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

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

Right Triangle

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

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.

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 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.

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 showing a triangle with a segment inside.

Triangle With Interior Segment Drawn

Illustration showing a triangle with a segment inside.

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.

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…

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 showing three triangles. This is used to show the following theorem: If two triangles have two sides of the one equal, respectively, to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Three Triangles Used to Compare Sides

Illustration showing three triangles. This is used to show the following theorem: If two triangles have…

Illustration showing an angle of 23 degrees 40 minutes making a triangle in a city block and marking off streets at 100 foot intervals.

Triangular City Block With Angles and Lengths

Illustration showing an angle of 23 degrees 40 minutes making a triangle in a city block and marking…

"In trigonometry, the arcs of circles are used to measure angles. All angles are supposed to have their vertexes at the center O of the circle, one side of the angle lying to the right of O, and coinciding with the horizontal diameter, as OB."

Arcs and Angles of a Trigonometric Circle

"In trigonometry, the arcs of circles are used to measure angles. All angles are supposed to have their…

Right triangle OCA, inside of Circle O is used to show that side AC is "opposite" O and side OC is "adjacent" to O. OA is the hypotenuse. Sine is defined as the ratio of the opposite side to the hypotenuse (AC/OA). Cosine is defined as the ratio of the adjacent side to the hypotenuse (OC/OA), and Tangent is defined as the ratio of the opposite side to the adjacent side (DB/OB).

Trigonometry Triangle to Show Sine, Cosine, and Tangent

Right triangle OCA, inside of Circle O is used to show that side AC is "opposite" O and side OC is "adjacent"…

Diagram used to prove the theorem: "The sum of two face angles of a trihedral angle is greater than the third."

Face Angles of Trihedral Angle

Diagram used to prove the theorem: "The sum of two face angles of a trihedral angle is greater than…

OP is a line representing a vector (directed quantity)

Vector

OP is a line representing a vector (directed quantity)

OP is a vector (directed quantity) showing the force by a weight acting on it at an angle of 20 degrees.

Vector Showing Force at Angle of 20 degrees

OP is a vector (directed quantity) showing the force by a weight acting on it at an angle of 20 degrees.