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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 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…

An illustration showing the construction used to divide an angle into two equal parts. "With C as a center, draw the dotted arc DE; with D and E as centers, draw the cross arcs at F with equal radii. Join CF, which divides the angle into the required parts."

Construction Of A Divided Angle

An illustration showing the construction used to divide an angle into two equal parts. "With C as a…

An illustration showing the construction used to divide an angle into two equal parts when the lines do not extend to a meeting point. "Draw the lined CD and CE parallel, and at equal distances from the lines AB and FG. With C as a center, draw the dotted arc BG; and with B and G as centers, draw the cross arcs H. Join CD, which divides the angle into the required equal parts."

Construction Of A Divided Angle

An illustration showing the construction used to divide an angle into two equal parts when the lines…

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…

Illustration where one leg of a right triangle is the diameter of a circle. The tangent at the point where the circumference cuts the hypotenuse bisects the other leg.

Circle With a Right Triangle

Illustration where one leg of a right triangle is the diameter of a circle. The tangent at the point…

Illustration showing that from any point in the circumference of a circle, a chord and a tangent are drawn, the perpendiculars dropped on them from the middle point of the subtended arc are equal.

Circle With a Tangent Line and Chord

Illustration showing that from any point in the circumference of a circle, a chord and a tangent are…

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 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 show how to bisect a straight line.

Bisect A Straight Line

Illustration used to show how to bisect a straight line.

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…