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Illustration used to show how to bisect a given arc.

Bisecting an Arc

Illustration used to show how to bisect a given arc.

Illustration used to show that "If two tangents are drawn from any given point to a circle, those tangents are equal."

Equal Tangents to Circle Theorem

Illustration used to show that "If two tangents are drawn from any given point to a circle, those tangents…

Illustration used to show that "A tangent to a circle is perpendicular to the radius drawn to the point of tangency."

Tangent to Perpendicular Radius Circle Theorem

Illustration used to show that "A tangent to a circle is perpendicular to the radius drawn to the point…

Illustration used to show that "The diameter perpendicular to a chord bisects the chord and also its subtended arc."

Diameter Perpendicular to a Chord in a Circle

Illustration used to show that "The diameter perpendicular to a chord bisects the chord and also its…

Illustration used to show that "In equal circles, or in the same circle, if two chords are equal, they subtend equal arcs; conversely, if two arcs are equal, the chords that subtend them are equal."

Equal Chords in Equal Circles Theorem

Illustration used to show that "In equal circles, or in the same circle, if two chords are equal, they…

Illustration used to show that "In equal circles, or in the same circle, if two chords are equal, they are equally distant from the center; conversely, if two chords are equally distant from the center, they are equal."

Equal Chords in Equal Circles Theorem

Illustration used to show that "In equal circles, or in the same circle, if two chords are equal, they…

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal, the greater chord subtends the greater minor arc; conversely, if two minor arcs are unequal, the chord that subtends the greater arc is the greater."

Unequal Chords in Circles Theorem

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal,…

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal, the greater chord is at the less distance from the center."

Unequal Chords in Equal Circles Theorem

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal,…

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal, the greater chord is at the less distance from the center."

Unequal Chords in Equal Circles Theorem

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal,…

Illustration used to prove the corollary that "Two lines perpendicular respectively to two intersecting lines also intersect."

Intersecting Lines Corollary

Illustration used to prove the corollary that "Two lines perpendicular respectively to two intersecting…

Illustration used to prove the corollary that "From a point outside a line there exists only one perpendicular to the line."

Perpendicular to Line Corollary

Illustration used to prove the corollary that "From a point outside a line there exists only one perpendicular…

"If from the foot of a perpendicular to a plane a straight line is drawn at right angles to any line in the lane, and its intersection with that line is joined to any point of the perpendicular, this last line will be perpendicular to the line in the plane."

Perpendicular To Line In Plane

"If from the foot of a perpendicular to a plane a straight line is drawn at right angles to any line…

"All the perpendiculars to a straight line at the same point lie in a plane perpendicular to the line."

Plane Perpendicular To Line

"All the perpendiculars to a straight line at the same point lie in a plane perpendicular to the line."

"Two planes perpendicular to the same straight line are parallel."

Planes Perpendicular To A Line

"Two planes perpendicular to the same straight line are parallel."

"Two straight lines perpendicular to the same plane are parallel."

Parallel Lines

"Two straight lines perpendicular to the same plane are parallel."

"Two straight lines that are parallel to a third are parallel to each other."

Parallel Lines

"Two straight lines that are parallel to a third are parallel to each other."

"If a straight line is perpendicular to each of two straight lines at their point of intersection it is perpendicular to the plane of those lines."

Line Perpendicular To Plane

"If a straight line is perpendicular to each of two straight lines at their point of intersection it…

"If one of two parallels is perpendicular to a plane, the other is also."

Lines Perpendicular To A Plane

"If one of two parallels is perpendicular to a plane, the other is also."

An illustration showing that the area of a regular polygon is equal to the area of a triangle whose base is equal to the sum of all the sides, and the height a equal to the appotem of the polygon. "The reason of this is that the area of two or more triangles ABC and ADC having a common or equal base b and equal height h are alike."

Area Of Regular Polygon Proof

An illustration showing that the area of a regular polygon is equal to the area of a triangle whose…

Illustration used to prove that "If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second."

2 Triangles Theorem

Illustration used to prove that "If two triangles have two sides of one equal respectively to two sides…

Illustration used to prove that "If two triangles have two sides of one equal respectively to two sides of the other, but the third side of the first greater than the third side of the second, then the angle opposite the third side of the first is greater than the angle opposite the third side of the second."

2 Triangles Theorem

Illustration used to prove that "If two triangles have two sides of one equal respectively to two sides…

Illustration used to prove that "If one side of a triangle is prolonged, the exterior angle formed is greater than either of the remote interior angles."

Exterior Angle of Triangle Theorem

Illustration used to prove that "If one side of a triangle is prolonged, the exterior angle formed is…

Illustration used to prove that "If two straight lines are parallel to a third straight line, they are parallel to each other."

Parallel Lines Theorem

Illustration used to prove that "If two straight lines are parallel to a third straight line, they are…

Illustration used to prove that "If two sides of a triangle are unequal, the angle opposite the greater side is greater than the angle opposite the less side."

Sides of Triangle Theorem

Illustration used to prove that "If two sides of a triangle are unequal, the angle opposite the greater…

Illustration used to prove that "The sum of any two sides of a triangle is greater than the third side."

Sides of Triangle Theorem

Illustration used to prove that "The sum of any two sides of a triangle is greater than the third side."

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…