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2 intersecting lines, one of which is vertical and one of which is horizontal. The intersection forms a right angle.

Intersecting Lines, 2 Perpendicular

2 intersecting lines, one of which is vertical and one of which is horizontal. The intersection forms…

Illustration to show that if an angle is bisected, and if a line drawn through the vertex perpendicular to the bisector, this line forms equal angles with the sides of the given angle.

Bisected Angle

Illustration to show that if an angle is bisected, and if a line drawn through the vertex perpendicular…

Illustration to show that the bisectors of two supplementary adjacent angles are perpendicular to each other.

Bisected Angles

Illustration to show that the bisectors of two supplementary adjacent angles are perpendicular to each…

Illustration to show that the bisector of one of two vertical angles bisects the other.

Bisected Angle

Illustration to show that the bisector of one of two vertical angles bisects the other.

Illustration to show that the bisector of two pairs of vertical angles formed by two intersecting lines are perpendicular to each other.

Bisected Angles

Illustration to show that the bisector of two pairs of vertical angles formed by two intersecting lines…

Illustration to show that the bisector of the vertical angle of an isosceles triangle bisects the base, and is perpendicular to the base.

Bisected Vertical Angle of an Isosceles Triangle

Illustration to show that the bisector of the vertical angle of an isosceles triangle bisects the base,…

Illustration used to show "The two perpendiculars to the sides of an angle from any point in its bisector are equal."

Perpendiculars To The Sides Of An Angle

Illustration used to show "The two perpendiculars to the sides of an angle from any point in its bisector…

Illustration used to show "The two perpendiculars to the sides of an angle from any point not in its bisector are unequal."

Perpendiculars To The Sides Of An Angle

Illustration used to show "The two perpendiculars to the sides of an angle from any point not in its…

An illustration showing when one straight line meets another straight line and makes the adjacent angles equal, each of these angles is called a right angle.

Right Angles With Same Vertex

An illustration showing when one straight line meets another straight line and makes the adjacent angles…

Angles used to illustrate the sum and difference of two angles and trig identities.

Angles Used to Illustrate Sum and Difference of Two Angles

Angles used to illustrate the sum and difference of two angles and trig identities.

Illustration showing angles 1 and 2 are supplementary and angles ACD and DCB are supplementary. Also, Angles ACD and DCB are right angles.

Supplementary and Right Angles

Illustration showing angles 1 and 2 are supplementary and angles ACD and DCB are supplementary. Also,…

Method to draw the bisector of a line

Bisect A Line

Method to draw the bisector of a line

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 of a circle with a tangent drawn - a straight line perpendicular to a radius at its extremity.

Circle With Tangent Line Drawn

Illustration of a circle with a tangent drawn - a straight line perpendicular to a radius at its extremity.

Illustration of the projection of a cone that is rightly inclined.

Projection Of Cone

Illustration of the projection of a cone that is rightly inclined.

Illustration of the construction used to bisect a given line.

Construction of Bisecting a Given Line

Illustration of the construction used to bisect a given line.

Illustration to let fall a perpendicular upon a given line from a given external point.

Construction of Perpendicular Upon a Given Line From an External Point

Illustration to let fall a perpendicular upon a given line from a given external point.

Illustration of the construction of a perpendicular to a line when given a point O on the straight line.

Construction of Perpendicular From a Given Point on a Straight Line

Illustration of the construction of a perpendicular to a line when given a point O on the straight line.

Illustration of the construction of a perpendicular to a line when given a point B on the straight line.

Construction of Perpendicular From a Given Point on a Straight Line

Illustration of the construction of a perpendicular to a line when given a point B on the straight line.

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 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…

Illustration of the projection of a cylinder that is rightly inclined.

Projection Of Cylinder

Illustration of the projection of a cylinder that is rightly inclined.

"The earth shown as it would be if its axis were perpendicular to the plane of the orbit." -Wiswell, 1913

Earth's Axis Perpendicular to Plane of Orbit

"The earth shown as it would be if its axis were perpendicular to the plane of the orbit." -Wiswell,…

Draftsman's fifth method for drawing an ellipse

Ellipse Fifth Method

Draftsman's fifth method for drawing an ellipse

Draftsman's fourth method for drawing an ellipse, case 1

Ellipse Fourth Method Case 1

Draftsman's fourth method for drawing an ellipse, case 1

Draftsman's fourth method for drawing an ellipse, case 2

Ellipse Fourth Method Case 2

Draftsman's fourth method for drawing an ellipse, case 2

A flashcard featuring a math symbol for Perpendicular

Flashcard of a math symbol for Perpendicular

A flashcard featuring a math symbol for Perpendicular

A flashcard featuring an illustration of Perpendicular Lines

Flashcard of Perpendicular Lines

A flashcard featuring an illustration of Perpendicular Lines

A line on the coordinate plane showing evidence of "perpendicular" form.

Perpendicular Form

A line on the coordinate plane showing evidence of "perpendicular" form.

A heraldic shield with a red (gules) surface, which is represented by the perpendicular lines, drawn from the head to the base of the shield.

Gules Shield

A heraldic shield with a red (gules) surface, which is represented by the perpendicular lines, drawn…

Illustration of the projection of a hexagonal pyramid that is in a right position.

Projection Of Hexagonal Pyramid

Illustration of the projection of a hexagonal pyramid that is in a right position.

Illustration modeling the illumination on a surface when the surface is not perpendicular to hte rays of light from a source of light.

Illumination of a Surface When the Surface is not Perpendicular to the Source

Illustration modeling the illumination on a surface when the surface is not perpendicular to hte rays…

Illustration of an extension ladder. If ladder is leaned against a building, it will form a right triangle with the ground.

Extension Ladder

Illustration of an extension ladder. If ladder is leaned against a building, it will form a right triangle…

Illustration of a ladder that is not perpendicular to the ground. If it is set on the ground and leaned toward a building, it will form the hypotenuse of a right triangle.

Leaning Ladder

Illustration of a ladder that is not perpendicular to the ground. If it is set on the ground and leaned…

Illustration of a ladder that is not perpendicular to the ground. If it is set on the ground and leaned toward a building, it will form the hypotenuse of a right triangle.

Leaning Ladder

Illustration of a ladder that is not perpendicular to the ground. If it is set on the ground and leaned…

Illustration of a ladder that is not perpendicular to the ground. If it is set on the ground and leaned toward a building, it will form the hypotenuse of a right triangle.

Leaning Ladder

Illustration of a ladder that is not perpendicular to the ground. If it is set on the ground and leaned…

Illustration of a ladder that is not perpendicular to the ground. If it is set on the ground and leaned toward a building, it will form the hypotenuse of a right triangle.

Leaning Ladder

Illustration of a ladder that is not perpendicular to the ground. If it is set on the ground and leaned…

Illustration of a ladder leaning against the side of a building (wall) to form a right triangle .

Ladder Leaning Against a Building

Illustration of a ladder leaning against the side of a building (wall) to form a right triangle .

Illustration of a ladder leaning against a palm tree, that is perpendicular to the ground, to form a right triangle .

Ladder Leaning Against a Tree

Illustration of a ladder leaning against a palm tree, that is perpendicular to the ground, to form a…

Illustration of a ladder leaning against a palm tree, that is perpendicular to the ground, to form a right triangle .

Ladder Leaning Against a Tree

Illustration of a ladder leaning against a palm tree, that is perpendicular to the ground, to form a…

Illustration of a ladder leaning against a palm tree, that is perpendicular to the ground, to form a right triangle .

Ladder Leaning Against a Tree

Illustration of a ladder leaning against a palm tree, that is perpendicular to the ground, to form a…

Illustration of a ladder leaning against a palm tree, that is perpendicular to the ground, to form a right triangle .

Ladder Leaning Against a Tree

Illustration of a ladder leaning against a palm tree, that is perpendicular to the ground, to form a…

Illustration of 2 ladders leaning against opposite sides of a palm tree to form similar right triangles. The angles of elevation from the ground to where the ladders meet the tree are congruent. Illustration can be used for problems involving proportions.

2 Ladders Leaning Against a Tree

Illustration of 2 ladders leaning against opposite sides of a palm tree to form similar right triangles.…

Illustration of 3 ladders leaning against the side of a building (wall) to form right triangles. The distance from the base of the ladders to the wall is the same for all three ladders.

3 Ladders Leaning Against a Wall

Illustration of 3 ladders leaning against the side of a building (wall) to form right triangles. The…

A Lemniscate is, in general, a curve generated by a point moving so that the product of its distances from two fixed points is the square of half the distance between the points. It is a particular case of the Cassinian oval and resembles a figure 8. When the line joining the two fixed points is the axis of x and the middle point of this line is the origin, the Cartesian equation is the fourth degree equation, (((x^2)+(y^2))^2)=2(a^2)((x^2)-(y^2)). The polar equation is (ℽ^2) = 2(a^2)cos(2θ). The locus of the feet of the perpendiculars from the center of an equilateral hyperbola to its tangents is a lemniscate. The name lemniscate is sometimes given to any crunodal symmetric quartic curve having no infinite branch. The name is also sometimes given to a general class of curves derived from other curves in the way that the above is derived from the equilateral hyperbola. With these more general definitions of the lemniscate the above curve is called the lemniscate of Bernoulli.

Lemniscate

A Lemniscate is, in general, a curve generated by a point moving so that the product of its distances…

Illustration showing a line that moves so that its ends constantly touch two fixed lines which are perpendicular to each other. Locus of the midpoint.

Circle Made by Ends of a Line Touching Two Fixed Lines Perpendicular to Each Other

Illustration showing a line that moves so that its ends constantly touch two fixed lines which are perpendicular…

Illustration showing that the perpendicular is the shortest line that can be drawn to a straight line from an external point.

Perpendicular Line Drawn To a Given Line From an External Point

Illustration showing that the perpendicular is the shortest line that can be drawn to a straight line…

Projections of a line perpendicular to a plane.

Projections of a Line

Projections of a line perpendicular to a plane.

Illustration showing two straight lines drawn from the same point in a perpendicular to a given line, cutting off on the line unequal segments from the foot of the perpendicular, the more remote is the greater.

Lines Drawn From the Same Point in a Perpendicular to a Given line, Cutting Off Segments

Illustration showing two straight lines drawn from the same point in a perpendicular to a given line,…

Illustration of two straight lines drawn from a point in a perpendicular to a given line, cutting off on the given line equal segments from the foot of the perpendicular, are equal and make equal angles with the perpendicular. This illustration can be used to show the proof.

Lines Drawn to Another Line to Form Triangle

Illustration of two straight lines drawn from a point in a perpendicular to a given line, cutting off…

Illustration showing only one perpendicular can be drawn to a given line from a given external point.

Perpendicular Line Drawn to a Given Line from an External Point

Illustration showing only one perpendicular can be drawn to a given line from a given external point.

Illustration showing two straight lines in the same plane perpendicular to the same straight line are parallel.

Parallel Lines

Illustration showing two straight lines in the same plane perpendicular to the same straight line are…

Illustration showing if a straight line is perpendicular to one of two parallel lines, it is perpendicular to the other also.

Parallel Lines

Illustration showing if a straight line is perpendicular to one of two parallel lines, it is perpendicular…

Draftsman's second method for drawing a parabola

Parabola Second Method

Draftsman's second method for drawing a parabola

Illustration showing two parallel vertical lines cut by a perpendicular line and a transversal. Congruent line segments are marked.

Parallel Lines Cut By a Perpendicular And Transversal

Illustration showing two parallel vertical lines cut by a perpendicular line and a transversal. Congruent…

The correct position when the pen is at the bottom of an extended letter below the line, the pen being, as shown, nearly perpendicular.

Penmanship

The correct position when the pen is at the bottom of an extended letter below the line, the pen being,…

A perpendicular line drawn from point P to straight line RS.

Perpendicular Line Drawn From Point P to Line RS

A perpendicular line drawn from point P to straight line RS.