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Illustration used to prove the theorem "If three or more parallel lines intercept equal segments on one transversal, they intercept equal segments on any other transversal."

4 Parallel Lines Cut By 2 Transversals

Illustration used to prove the theorem "If three or more parallel lines intercept equal segments on…

Illustration of a circle with parallels intercepting equal arcs on a circumference.

Circles With Parallels Intercepting Equal Arcs

Illustration of a circle with parallels intercepting equal arcs on a circumference.

Illustration used to show how to divide a given straight line into any number of equal parts.

Line Divided Into Equal Parts

Illustration used to show how to divide a given straight line into any number of equal parts.

"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."

Illustration of parallel lines.

Parallel Lines

Illustration of parallel lines.

"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."

Illustration used to prove "The line joining the mid-points of two sides of a triangle is parallel to the third side and equal to one half the third side."

Line Joining Midpoints on a Triangle

Illustration used to prove "The line joining the mid-points of two sides of a triangle is parallel to…

An illustration showing the construction used to erect a parallel line. "With C as a center, draw the dotted arc ED, with E as a center, draw through C the dotted arc F.C. With the radius FC and E as a center, draw the cross arc at D. Join C with the cross at D, which will be the required parallel line.

Construction Of A Parallel

An illustration showing the construction used to erect a parallel line. "With C as a center, draw the…

"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."

Illustration of three intersecting planes. "The intersections of two parallel planes by a third plane are parallel lines."

3 Intersecting Planes

Illustration of three intersecting planes. "The intersections of two parallel planes by a third plane…

Illustration of three intersecting planes. "The straight line perpendicular to one of two parallel lanes is perpendicular to the other."

3 Intersecting Planes

Illustration of three intersecting planes. "The straight line perpendicular to one of two parallel lanes…

"If two straight lines are cut by three parallel planes, the corresponding segments are proportional."

3 Parallel Planes

"If two straight lines are cut by three parallel planes, the corresponding segments are proportional."

"If two angles not in the same plane have their sides respectively parallel and lying in the same direction, they are equal and their planes are parallel."

Angles In Parallel Planes

"If two angles not in the same plane have their sides respectively parallel and lying in the same direction,…

"If two intersecting lines are each parallel to a given plane, the plane of these lines is parallel to the given plane."

Parallel Planes

"If two intersecting lines are each parallel to a given plane, the plane of these lines is parallel…

Illustration used to prove "The line bisecting one side of a triangle and parallel to another side bisects the third side."

Line Bisecting Side of a Triangle

Illustration used to prove "The line bisecting one side of a triangle and parallel to another side bisects…

Illustration used to prove the theorem "The line bisecting one of the non parallel sides of a trapezoid and parallel to the bases bisects the other of the non parallel sides also."

Line Bisecting Trapezoid Sides

Illustration used to prove the theorem "The line bisecting one of the non parallel sides of a trapezoid…