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Illustration showing how to construct the bisector of an angle.

Construction Of Angle Bisector

Illustration showing how to construct the bisector of an angle.

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 of a dihedral angle bisected by a plane. "Every point in a plane which bisects a dihedral angle is equidistant from the faces of the angle."

Dihedral Angle With Bisector

Illustration of a dihedral angle bisected by a plane. "Every point in a plane which bisects a dihedral…

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 to show that if through any point in the bisector of an angle a line is drawn parallel to either of the sides of the angle, the triangle thus formed is isosceles.

Angle Bisector Drawn Parallel to A Side

Illustration to show that if through any point in the bisector of an angle a line is drawn parallel…

Illustration used to show how to bisect a given arc.

Bisecting an Arc

Illustration used to show how to bisect a given arc.

Illustration of a circle with diameter and chord drawn. A diameter perpendicular to a chord bisects the chord and the arcs subtended by it.

Circle With Diameter and Chord

Illustration of a circle with diameter and chord drawn. A diameter perpendicular to a chord bisects…

Method to construct an isosceles triangle

Construct Isosceles Triangle

Method to construct an isosceles triangle

Method to construct a scalene triangle

Construct Scalene Triangle

Method to construct a scalene triangle

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 bisect a given arc.

Construction of Bisecting a Given Arc

Illustration of the construction used to bisect a given arc.

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 of the construction used to escribe circles with centres (centers) called ex-centres of the triangles. The intersections of the bisectors of the exterior angles of a triangle are the centers of three circles, each of which will touch one side of the triangle, and the two other circles.

Construction of Escribed Circles With Ex-centres

Illustration of the construction used to escribe circles with centres (centers) called ex-centres of…

Draftsman's first method for creating an ellipse

Ellipse First Method

Draftsman's first method for creating an ellipse

Illustration of half of an ellipse. "If through a point P of an ellipse a line is drawn bisecting the angle between one of the focal radii and the other produced, every point in this line except P is without the curve."

Line Bisecting Angle Between Focal Radii on Ellipse

Illustration of half of an ellipse. "If through a point P of an ellipse a line is drawn bisecting the…

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…

Illustration of a parallelogram with diagonals drawn to show they bisect each other.

Parallelogram With Diagonals Bisecting Each Other

Illustration of a parallelogram with diagonals drawn to show they bisect each other.

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 to show that the bisector of an exterior angle of an isosceles triangle, formed by producing one of the legs through the vertex, is parallel o the base.

Bisector of an Exterior Angle of an Isosceles Triangle

Illustration to show that the bisector of an exterior angle of an isosceles triangle, formed by producing…

Illustration of a triangle showing that when a line parallel to the base of a triangle bisects one side, it bisects the other side also.

Triangle With Bisector Parallel to the Base

Illustration of a triangle showing that when a line parallel to the base of a triangle bisects one side,…

Illustration to show that if one of the legs of an isosceles triangle is produced through the vertex by its own length, the line joining he end of the leg produced to the nearer end of the base is perpendicular to the base.

Leg Produced through the Vertex of an Isosceles Triangle

Illustration to show that if one of the legs of an isosceles triangle is produced through the vertex…

Illustration to show that if the lines joining the middle points of the sides of a triangle divide the triangle into four equal triangles.

Midpoints of Triangle Divide Triangle into Four Equal Triangles

Illustration to show that if the lines joining the middle points of the sides of a triangle divide the…

Illustration to show that the perpendicular bisector of the base of an isosceles triangle passes through the vertex and bisects the angle at the vertex.

Perpendicular Bisector of the Base of an Isosceles Triangle

Illustration to show that the perpendicular bisector of the base of an isosceles triangle passes through…