 ### Bisecting an Arc

Illustration used to show how to bisect a given arc. ### Angle Bisector

Illustration showing that the bisector of a given angle is the locus of points equidistant from the… ### Perpendicular Bisector of a Line

Illustration showing that the perpendicular bisector of a given line is the locus of points equidistant… ### Equal Tangents to Circle Theorem

Illustration used to show that "If two tangents are drawn from any given point to a circle, those tangents… ### 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… ### 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… ### 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… ### 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… ### Unequal Chords in Circles Theorem

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal,… ### Unequal Chords in Equal Circles Theorem

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal,… ### Unequal Chords in Equal Circles Theorem

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

Illustration used to prove the corollary that "Two lines perpendicular respectively to two intersecting… ### Perpendicular to Line Corollary

Illustration used to prove the corollary that "From a point outside a line there exists only one perpendicular… ### Model Of Geometric Proportions In A Circle

An illustration showing a model of a circle with intersecting chords that illustrates the following… ### Model Of Geometric Proportions In A Triangle

An illustration showing a model of a triangle that illustrates the following relationship: a:c = d:(b… ### Model Of Geometric Proportions

An illustration showing a quadrilateral model that illustrates the following relationships: a:b = c:d,… ### Model Of Geometric Proportions

An illustration showing a model that illustrates the following relationships: a:b = c:d, ad = bc. Product… ### Model Of Geometric Proportions

An illustration showing a model that illustrates the following relationships: a:b = c:b, ab = c²,… ### Model Of Geometric Proportions

An illustration showing a model that illustrates the following relationship: A:B = a:b. ### Model Of Geometric Proportions

An illustration showing a model that illustrates the following relationships: a:x = x:a - x, x = √(a²… ### Model Of Geometric Relationships In 2 Circles

An illustration showing a model of 2 circles with tangent lines, diameters, and radii that illustrates… ### Model Of Geometric Relationships In 2 Circles

An illustration showing a model of 2 circles with tangent lines, diameters, and radii that illustrates… ### Model Of Geometric Relationships In A Circle

An illustration showing a model of a circle with an exterior angle formed between a tangent and a secant… ### Model Of Geometric Relationships In A Circle

An illustration showing a model of a circle with angles formed between tangents and secants that illustrates… ### 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… ### Plane Perpendicular To Line

"All the perpendiculars to a straight line at the same point lie in a plane perpendicular to the line." ### Planes Perpendicular To A Line

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

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

"Two straight lines that are parallel to a third are parallel to each other." ### Line Perpendicular To Plane

"If a straight line is perpendicular to each of two straight lines at their point of intersection it… ### Lines Perpendicular To A Plane

"If one of two parallels is perpendicular to a plane, the other is also." ### 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… ### Exterior Angle Proof

Illustration used to prove "An exterior angle of a triangle is equal to the sum of the two remote interior… ### 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… ### 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… ### Area Of Regular Polygon Proof

An illustration showing that the area of a regular polygon is equal to the area of a triangle whose… ### 2 Triangles Theorem

Illustration used to prove that "If two triangles have two sides of one equal respectively to two sides… ### 2 Triangles Theorem

Illustration used to prove that "If two triangles have two sides of one equal respectively to two sides… ### Exterior Angle of Triangle Theorem

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

Illustration used to prove that "If two straight lines are parallel to a third straight line, they are… ### Sides of Triangle Theorem

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

Illustration used to prove that "The sum of any two sides of a triangle is greater than the third side." ### Segments Labeled In A Triangle

Illustration of triangle ABC with BE extended through the triangle at point D. Segment AB is equal to… ### Three Triangles Used to Compare Sides

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