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Illustration of a circle used to prove "All angles inscribed in the same segment are equal."

Angles Inscribed in the Same Segment Circle Proof

Illustration of a circle used to prove "All angles inscribed in the same segment are equal."

Illustration of a circle with an inscribed angle that can be used to prove that "An inscribed angle is measured by one half of its intercepted arc." In this case, one side of angle ABC passes through the center of the circle.

Inscribed Angle in a Circle Proof

Illustration of a circle with an inscribed angle that can be used to prove that "An inscribed angle…

Illustration of a circle with an inscribed angle that can be used to prove that "An inscribed angle is measured by one half of its intercepted arc." In this case, center O lies within angle ABC.

Inscribed Angle in a Circle Proof

Illustration of a circle with an inscribed angle that can be used to prove that "An inscribed angle…

Illustration of a circle with an inscribed angle that can be used to prove that "An inscribed angle is measured by one half of its intercepted arc." In this case, center O lies outside angle ABC.

Inscribed Angle in a Circle Proof

Illustration of a circle with an inscribed angle that can be used to prove that "An inscribed angle…

Illustration of a circle used to prove "Any angle inscribed in a segment less than a semicircle is an obtuse angle."

Obtuse Angles Inscribed in Circle Proof

Illustration of a circle used to prove "Any angle inscribed in a segment less than a semicircle is an…

Illustrations of a circle with arc, chord, inscribed angle, and circumscribed about a polygon.

Circle with Arc, Chord, Inscribed Angle, Circumscribed Polygon

Illustrations of a circle with arc, chord, inscribed angle, and circumscribed about a polygon.

Illustration of a circle with central angle AOB.

Central Angle in a Circle

Illustration of a circle with central angle AOB.

Illustration of a circle that can be used to show that an "angle at the center of a circle is measured by its intercepted arc."

Central Angles and Arcs in a Circle

Illustration of a circle that can be used to show that an "angle at the center of a circle is measured…

Illustration of a circle that can be used to show that an "angle at the center of a circle is measured by its intercepted arc." Angle AOB and angle COE are commensurable.

Central Angles and Arcs in a Circle

Illustration of a circle that can be used to show that an "angle at the center of a circle is measured…

Illustration of a circle that can be used to show that an "angle at the center of a circle is measured by its intercepted arc." Angle AOB and angle COE are incommensurable.

Central Angles and Arcs in a Circle

Illustration of a circle that can be used to show that an "angle at the center of a circle is measured…

Illustration of a circle showing an angle included by a tangent and a chord drawn from the point of contact. The angle is measured by half the intercepted arc.

Circle With Chord and Tangent

Illustration of a circle showing an angle included by a tangent and a chord drawn from the point of…

Illustration of a circle with an angle inscribed in a segment greater than a semicircle, an acute angle.

Circle With Inscribed Angle Greater Than Semicircle

Illustration of a circle with an angle inscribed in a segment greater than a semicircle, an acute angle.

Illustration of a circle with an inscribed angle.

Inscribed Angle in a Circle

Illustration of a circle with an inscribed angle.

Illustration of a circle with an angle inscribed in a segment less than a semicircle, an obtuse angle.

Circle With Inscribed Angle Less Than Semicircle

Illustration of a circle with an angle inscribed in a segment less than a semicircle, an obtuse angle.

Illustration of a circle with a right angle inscribed in a semicircle.

Circle With Inscribed Right Angle in Semicircle

Illustration of a circle with a right angle inscribed in a semicircle.

Illustration of a circle with two intersecting chords within the circumference. The angle formed is measured by half the sum of the intercepted arcs.

Circle With Two Intersecting Chords

Illustration of a circle with two intersecting chords within the circumference. The angle formed is…

Illustration showing angles formed by two secants, two tangents, or a tangent and a secant, drawn to a circle form an external point. The angle is measured by half the difference of the intercepted arcs.

Circles With Angles Formed by Secants and Tangents

Illustration showing angles formed by two secants, two tangents, or a tangent and a secant, drawn to…

Illustration of equal circles to show that an inscribed angle is measured by half the arc intercepted between its sides.

Circles With Inscribed Angles

Illustration of equal circles to show that an inscribed angle is measured by half the arc intercepted…

Illustration showing various circles and the angles formed by intersecting lines.

Intersecting Lines in Circles

Illustration showing various circles and the angles formed by intersecting lines.

A pilot's cockpit from a propeller aeroplane, or airplane. The diagram illustrates the different parts of the cockpit used to control the plane. The cockpit contains gauges; watch; joystick controlling ailerons and elevators; and wires to adjust wings.

Aeroplane Cockpit

A pilot's cockpit from a propeller aeroplane, or airplane. The diagram illustrates the different parts…

Illustration of the construction used to bisect a given angle.

Construction of Bisecting a Given Angle

Illustration of the construction used to bisect a given angle.

Illustration of the construction used to create an equal angle given a point in a given straight line and a given angle.

Construction of an Equal Angle Given a Point and a Straight Line

Illustration of the construction used to create an equal angle given a point in a given straight line…

Illustration of the construction used to find the third angle of a triangle when two of the angles are given.

Construction to Find the Third Angle of a Triangle When Given Two Angles

Illustration of the construction used to find the third angle of a triangle when two of the angles are…

Illustration of the construction used to make a parallelogram when given two sides and the included angle.

Construction of a Parallelogram When Given Two Sides and Included Angle

Illustration of the construction used to make a parallelogram when given two sides and the included…

Illustration of the construction used to make a triangle when given two sides and the angle opposite one of them. This is for case 1 of the ambiguous case, when a is less than b.

Construction of a Triangle When Given Two Sides and the Angle Opposite (Ambiguous Case)

Illustration of the construction used to make a triangle when given two sides and the angle opposite…

Illustration of the construction used to make a triangle when given two sides and the angle opposite one of them. This is for case 2 of the ambiguous case, when a is equal to b.

Construction of a Triangle When Given Two Sides and the Angle Opposite (Ambiguous Case)

Illustration of the construction used to make a triangle when given two sides and the angle opposite…

Illustration of the construction used to make a triangle when given two sides and the angle opposite one of them. This is for case 2 of the ambiguous case, when a is equal to b.

Construction of a Triangle When Given Two Sides and the Angle Opposite (Ambiguous Case)

Illustration of the construction used to make a triangle when given two sides and the angle opposite…

Illustration of the construction used to make a triangle when given two sides and the included angle.

Construction of a Triangle When Given Two Sides and Included Angle

Illustration of the construction used to make a triangle when given two sides and the included angle.

Coordinate axis with angle XOP equal to theta, Θ, and angle XOQ=180 - Θ. From any point in the terminal side of XOP, as B, a perpendicular can be drawn, AB, to the x-axis; and from D, any point in the terminal side o f XOQ, perpendicular CD can be drawn to the x-axis. The right triangles OAB and OCD are similar. Also, OA, AB, OB, CD, and OD are positive, while OC is negative.

Coordinate Axis With Angles, Lines, and Perpendiculars Drawn

Coordinate axis with angle XOP equal to theta, Θ, and angle XOQ=180 - Θ. From any point in the terminal…

Angle XOP=Θ and angle XOQ=- Θ. From a point in the terminal side of each a perpendicular line is drawn to the x-axis. The right triangles OAB and OAC thus formed are similar, and have all their sides positive except AC, which is negative.

Coordinate Axis With Perpendiculars Drawn To Form Similar Right Triangles From Positive and Negative Theta, Θ

Angle XOP=Θ and angle XOQ=- Θ. From a point in the terminal side of each a perpendicular line is drawn…

Angle XOP=Θ and angle XOQ=90+Θ. From a point in the terminal side of each a perpendicular line is drawn to the x-axis. The right triangles AOB and OCD thus formed are similar, and have all their sides positive except OC

Coordinate Axis With Perpendiculars Drawn To Form Similar Right Triangles

Angle XOP=Θ and angle XOQ=90+Θ. From a point in the terminal side of each a perpendicular line is…

Illustration showing coterminal angles of 0° and -360°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, both angles are labeled with the proper degree measure.

0° and -360° Coterminal Angles

Illustration showing coterminal angles of 0° and -360°. Coterminal angles are angles drawn in…

Illustration showing coterminal angles of 0° and -360°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, neither angle is labeled.

0° and -360° Coterminal Angles

Illustration showing coterminal angles of 0° and -360°. Coterminal angles are angles drawn in…

Illustration showing coterminal angles of 0° and -360°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the negative angle is labeled with the proper degree measure.

0° and -360° Coterminal Angles

Illustration showing coterminal angles of 0° and -360°. Coterminal angles are angles drawn in…

Illustration showing coterminal angles of 0° and -360°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

0° and -360° Coterminal Angles

Illustration showing coterminal angles of 0° and -360°. Coterminal angles are angles drawn in…

Illustration showing coterminal angles of 10° and -350°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, both angles are labeled with the proper degree measure.

10° and -350° Coterminal Angles

Illustration showing coterminal angles of 10° and -350°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 10° and -350°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, neither angle is labeled.

10° and -350° Coterminal Angles

Illustration showing coterminal angles of 10° and -350°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 10° and -350°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the negative angle is labeled with the proper degree measure.

10° and -350° Coterminal Angles

Illustration showing coterminal angles of 10° and -350°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 10° and -350°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

10° and -350° Coterminal Angles

Illustration showing coterminal angles of 10° and -350°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 100° and -260°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, both angles are labeled with the proper degree measure.

100° and -260° Coterminal Angles

Illustration showing coterminal angles of 100° and -260°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 100° and -260°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, neither angle is labeled.

100° and -260° Coterminal Angles

Illustration showing coterminal angles of 100° and -260°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 100° and -260°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the negative angle is labeled with the proper degree measure.

100° and -260° Coterminal Angles

Illustration showing coterminal angles of 100° and -260°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 100° and -260°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

100° and -260° Coterminal Angles

Illustration showing coterminal angles of 100° and -260°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 105° and -255°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, both angles are labeled with the proper degree measure.

105° and -255° Coterminal Angles

Illustration showing coterminal angles of 105° and -255°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 105° and -255°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, neither angle is labeled.

105° and -255° Coterminal Angles

Illustration showing coterminal angles of 105° and -255°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 105° and -255°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the negative angle is labeled with the proper degree measure.

105° and -255° Coterminal Angles

Illustration showing coterminal angles of 105° and -255°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 105° and -255°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

105° and -255° Coterminal Angles

Illustration showing coterminal angles of 105° and -255°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 110° and -250°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, both angles are labeled with the proper degree measure.

110° and -250° Coterminal Angles

Illustration showing coterminal angles of 110° and -250°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 110° and -250°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, neither angle is labeled.

110° and -250° Coterminal Angles

Illustration showing coterminal angles of 110° and -250°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 110° and -250°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the negative angle is labeled with the proper degree measure.

110° and -250° Coterminal Angles

Illustration showing coterminal angles of 110° and -250°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 110° and -250°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

110° and -250° Coterminal Angles

Illustration showing coterminal angles of 110° and -250°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 115° and -245°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, both angles are labeled with the proper degree measure.

115° and -245° Coterminal Angles

Illustration showing coterminal angles of 115° and -245°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 115° and -245°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, neither angle is labeled.

115° and -245° Coterminal Angles

Illustration showing coterminal angles of 115° and -245°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 115° and -245°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the negative angle is labeled with the proper degree measure.

115° and -245° Coterminal Angles

Illustration showing coterminal angles of 115° and -245°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 115° and -245°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

115° and -245° Coterminal Angles

Illustration showing coterminal angles of 115° and -245°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 120° and -240°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, both angles are labeled with the proper degree measure.

120° and -240° Coterminal Angles

Illustration showing coterminal angles of 120° and -240°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 120° and -240°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, neither angle is labeled.

120° and -240° Coterminal Angles

Illustration showing coterminal angles of 120° and -240°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 120° and -240°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the negative angle is labeled with the proper degree measure.

120° and -240° Coterminal Angles

Illustration showing coterminal angles of 120° and -240°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 120° and -240°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

120° and -240° Coterminal Angles

Illustration showing coterminal angles of 120° and -240°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 125° and -235°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, both angles are labeled with the proper degree measure.

125° and -235° Coterminal Angles

Illustration showing coterminal angles of 125° and -235°. Coterminal angles are angles drawn…