Illustration used to prove "Two angles whose sides are perpendicular each to each are either equal or supplementary."

Angles With Perpendicular Sides Are Equal or Supplementary Proof

Illustration used to prove "Two angles whose sides are perpendicular each to each are either equal or…

Illustration used to prove "An exterior angle of a triangle is equal to the sum of the two remote interior angles."

Exterior Angle Proof

Illustration used to prove "An exterior angle of a triangle is equal to the sum of the two remote interior…

Illustration used to prove "If the sides of any polygon are prolonged in succession one way, no two adjacent sides being prolonged through the same vertex, the sum of the exterior angles thus formed is four right angles."

Sum of Exterior Angles of a Polygon Proof

Illustration used to prove "If the sides of any polygon are prolonged in succession one way, no two…

Illustration used to prove "The sum of all the angles of any polygon is twice as many right angles as the polygon has sides, less four right angles."

Sum of Interior Angles of a Polygon Proof

Illustration used to prove "The sum of all the angles of any polygon is twice as many right angles as…

A math tool used for measuring angles on blueprints.

Protractor

A math tool used for measuring angles on blueprints.

A 6 inches diameter protractor to measure angles to half degrees, made of brass or German silver. They are useful in map and topographical work.

Semicircular Protractor

A 6 inches diameter protractor to measure angles to half degrees, made of brass or German silver. They…

Illustration showing that the volume of 2 triangular pyramids, having the same trihedral angle of the one equal to a trihedral angle of the other, are to each other as the products of the three edges of these trihedral angles.

Triangular Pyramids for Volume

Illustration showing that the volume of 2 triangular pyramids, having the same trihedral angle of the…

Illustration of an angle &alpha with the vertex at the center, O, of a circle with radius OB. AC and BD are perpendicular to OB and join B with C. The are of the triangle OBC is less than the are of the sector OBC, and the sector OBC is less than the triangle OBD.

Triangles and Sectors in Quadrant I

Illustration of an angle &alpha with the vertex at the center, O, of a circle with radius OB. AC and…

Illustration of an angle &alpha with the terminal side used to draw a triangle in quadrant I.

Triangle in Quadrant I

Illustration of an angle &alpha with the terminal side used to draw a triangle in quadrant I.

Illustration of an angle with the terminal side used to draw a triangle in quadrant II.

Triangle in Quadrant II

Illustration of an angle with the terminal side used to draw a triangle in quadrant II.

A printers quoin is a device for locking up or fastening type in chases or galleys.

Printers Quoin

A printers quoin is a device for locking up or fastening type in chases or galleys.

A detached triangular work in fortification, with two embankments which form a projecting angle. In the figure B B is the ravelin with A its redout, and CC its ditch, DD being the main ditch of the fortress,and E the passage giving access from the fortress to the ravelin.

Ravelin

A detached triangular work in fortification, with two embankments which form a projecting angle. In…

Rectangle with angles labeled. Parallelogram with right angles.

Rectangle

Rectangle with angles labeled. Parallelogram with right angles.

In field fortification, the simplest kind of work employed, consisting of two parapets of earth raised so as to form a salient angle, with the apex towards the enemy and unprotected on the rear. Several redans connected by curtains form lines of intrenchment.

Redans

In field fortification, the simplest kind of work employed, consisting of two parapets of earth raised…

"The angle, ABD, included between the direction of the moving body before it strikes the reflecting surface, and a perpendicular to that surface drawn from the point of contact, is called the angle of incidence. The angle between the perpendicular and the direction of the moving body after striking is called the angle of reflection." -Avery 1895

Law of Reflected Motion

"The angle, ABD, included between the direction of the moving body before it strikes the reflecting…

"... if a ball be thrown from F against the surface B C so as to strike it perpendicularly at A, it will return in the line A F. If thrown from D however, it will glance off on the other side of the perpendicular, at the same angle, to E." —Quackenbos 1859

Reflected Motion

"... if a ball be thrown from F against the surface B C so as to strike it perpendicularly at A, it…

"Angle of incidence equals angle of reflection." —Croft 1917

Reflection of Light

"Angle of incidence equals angle of reflection." —Croft 1917

"The ray a, c, is the ray of incidence, and that from c, to d, is the ray or reflection. The angles which a, c, make with the perpendicular line, and with the plane of the mirror, is exactly equal to those made by c, d, with the same perpendicular, and the same plane surface." -Comstock 1850

Reflection of Light

"The ray a, c, is the ray of incidence, and that from c, to d, is the ray or reflection. The angles…

Illustration used to show "If one acute angle of a right triangle is double the other, the hypotenuse is double the shorter side."

Relationships In A Right Triangle

Illustration used to show "If one acute angle of a right triangle is double the other, the hypotenuse…

Roof with a slope of 30 degrees. Angle theta is the inclination to the horizontal of the line AB, drawn in the roof and making an angle of 35 degrees with the line of greatest slope.

Roof With 30 degree Inclination for Trigonometry Triangle Problems

Roof with a slope of 30 degrees. Angle theta is the inclination to the horizontal of the line AB, drawn…

A propeller airplane with rudder, elevator, and ailerons. The rudder stabilizes the plane vertical, and elevator adjusts the pressure exerted by the horizontal stabilizer for a downward force.

Airplane Rudder and Elevator

A propeller airplane with rudder, elevator, and ailerons. The rudder stabilizes the plane vertical,…

Illustration two types of triangles that can be used to model the law of sines. "In a plane triangle any two sides are to each other as the sines of the opposite angles."

Law of Sines

Illustration two types of triangles that can be used to model the law of sines. "In a plane triangle…

Illustration of a right spherical triangle and the five circular parts placed in the sectors of a circle in the order in which they occur in the triangle. "The ten formulas used in the solution of spherical right triangles can be expressed by means of two rules, known as Napier's rules of circular parts."

Napier's Right Spherical Triangle

Illustration of a right spherical triangle and the five circular parts placed in the sectors of a circle…

Illustration used, with the law of sines, to find the relation between two sides of a spherical triangle and the angles opposite.

Relationships In A Spherical Triangle

Illustration used, with the law of sines, to find the relation between two sides of a spherical triangle…

Illustration used, with the law of cosines, to find the relation between the three sides and an angle of a spherical triangle.

Relationships In A Spherical Triangle

Illustration used, with the law of cosines, to find the relation between the three sides and an angle…

Illustration used to extend the law of cosines when finding the relation between the three sides and an angle of a spherical triangle. In this case both angles b and c are greater than 90°.

Relationships In A Spherical Triangle

Illustration used to extend the law of cosines when finding the relation between the three sides and…

Illustration used to extend the law of cosines when finding the relation between the three sides and an angle of a spherical triangle. In this case angle b<90&deg; and angle c>90&deg;.

Relationships In A Spherical Triangle

Illustration used to extend the law of cosines when finding the relation between the three sides and…

Illustration of a right spherical triangle with a and b the sides, and &alpha; and &beta; the angles opposite them. Side c is the hypotenuse.

Right Spherical Triangle

Illustration of a right spherical triangle with a and b the sides, and α and β the angles…

Square with angles labeled. A rectangle with four equal sides.

Square

Square with angles labeled. A rectangle with four equal sides.

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, &#398; 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 showing a survey on the lake front in Chicago with distances and angle measures shown.

Survey of Lake Front in Chicago

Illustration showing a survey on the lake front in Chicago with distances and angle measures shown.

The angle ornament symbol is a symbol of art.

Angle Ornament Symbol

The angle ornament symbol is a symbol of art.

"An instrument for the measurement of horizontal angles, consisting essentially of a telescope mounted so as to move on a pivot both horizontal and verticaly." &mdash; Williams, 1889

Theodolite

"An instrument for the measurement of horizontal angles, consisting essentially of a telescope mounted…

"An instrument much employed in land-surveying for the measurement of angles horizontal and verticle." &mdash; Chambers, 1881

Theodolite

"An instrument much employed in land-surveying for the measurement of angles horizontal and verticle."…

Trapezoid with angles and height labeled.

Trapezoid

Trapezoid with angles and height labeled.

Triangle diagram for measuring heights of trees using proportions.

Using Proportions To Find Heights of Trees

Triangle diagram for measuring heights of trees using proportions.

Triangle diagram for measuring heights of trees using proportions

Using Proportions To Find Heights of Trees

Triangle diagram for measuring heights of trees using proportions

Illustration used to construct a triangle given the length of the base and the two base angles.

Construction of Triangle Given Angles and Base

Illustration used to construct a triangle given the length of the base and the two base angles.

Illustration showing a triangle with angles A, B, and C labeled.

Triangle ABC

Illustration showing a triangle with angles A, B, and C labeled.

Illustration showing an acute triangle (one that has all three angles that are acute).

Acute Triangle

Illustration showing an acute triangle (one that has all three angles that are acute).

Illustration to show altitudes drawn from base angles of an isosceles triangle.

Altitudes Drawn from Base Angles of Isosceles Triangles

Illustration to show altitudes drawn from base angles of an isosceles triangle.

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

Angle Bisectors In A Triangle

Illustration used to prove "The bisectors of the angles of a triangle are concurrent in a point which…

Illustration to show that the bisector of an exterior angle of an isosceles triangle, formed by producing one of the legs through the vertex, is parallel o the base.

Bisector of an Exterior Angle of an Isosceles Triangle

Illustration to show that the bisector of an exterior angle of an isosceles triangle, formed by producing…

Illustration to show medians in a triangle. It is known as the centroid.

Centroid of Triangle

Illustration to show medians in a triangle. It is known as the centroid.

Illustration to show perpendicular bisectors in a triangle. It is known as the circumcenter.

Circumcenter of Triangle

Illustration to show perpendicular bisectors in a triangle. It is known as the circumcenter.

Illustration showing an equiangular triangle (one that has all three angles that are equal).

Equiangular Triangle

Illustration showing an equiangular triangle (one that has all three angles that are equal).

An illustration showing a triangle with interior angles A, B, C, and exterior angles D, and A' + B'.

Exterior And Interior Angles Of A Triangle

An illustration showing a triangle with interior angles A, B, C, and exterior angles D, and A' + B'.

Illustration showing a triangle with exterior angles. This can be used to show the sum of the three angles of a triangle is equal to two right angles.

Triangle with Exterior Angles Drawn

Illustration showing a triangle with exterior angles. This can be used to show the sum of the three…

Illustration to show angle bisectors in a triangle. It is known as the incenter.

Incenter of Triangle

Illustration to show angle bisectors in a triangle. It is known as the incenter.

Inclined plane using right triangle and proportions

Inclined Plane Triangle

Inclined plane using right triangle and proportions

An isosceles triangle with angles 1, 89.5, 89.5

Isosceles Triangle degrees 1, 89.5, 89.5

An isosceles triangle with angles 1, 89.5, 89.5

An isosceles triangle with angles 10, 85, 85

Isosceles Triangle degrees 10, 85, 85

An isosceles triangle with angles 10, 85, 85

An isosceles triangle with angles 100, 40, 40

Isosceles Triangle degrees 100, 40, 40

An isosceles triangle with angles 100, 40, 40

An isosceles triangle with angles 101, 39.5, 39.5

Isosceles Triangle degrees 101, 39.5, 39.5

An isosceles triangle with angles 101, 39.5, 39.5

An isosceles triangle with angles 102, 39, 39

Isosceles Triangle degrees 102, 39, 39

An isosceles triangle with angles 102, 39, 39

An isosceles triangle with angles 103, 38.5, 38.5

Isosceles Triangle degrees 103, 38.5, 38.5

An isosceles triangle with angles 103, 38.5, 38.5

An isosceles triangle with angles 104, 38, 38

Isosceles Triangle degrees 104, 38, 38

An isosceles triangle with angles 104, 38, 38

An isosceles triangle with angles 105, 37.5, 37.5

Isosceles Triangle degrees 105, 37.5, 37.5

An isosceles triangle with angles 105, 37.5, 37.5

An isosceles triangle with angles 106, 37, 37

Isosceles Triangle degrees 106, 37, 37

An isosceles triangle with angles 106, 37, 37

An isosceles triangle with angles 107, 36.5, 36.5

Isosceles Triangle degrees 107, 36.5, 36.5

An isosceles triangle with angles 107, 36.5, 36.5