Illustration to show altitudes in a triangle. It is known as the orthocenter.

Orthocenter of Triangle

Illustration to show altitudes in a triangle. It is known as the orthocenter.

Illustration to show medians in a triangle. It is known as the centroid.

Centroid of Triangle

Illustration to show medians in a triangle. It is known as the centroid.

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 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…

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 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 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 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 altitudes drawn from base angles of an isosceles triangle.

Altitudes Drawn from Base Angles of Isosceles Triangles

Illustration to show altitudes drawn from base angles of an isosceles triangle.

Illustration to show the medians drawn to the legs of an isosceles triangle.

Medians Drawn Drawn to Legs of Isosceles Triangles

Illustration to show the medians drawn to the legs of an isosceles triangle.

Illustration to show the perpendiculars dropped from the midpoint of the base to the legs of an isosceles triangle are equal.

Perpendiculars Dropped From Midpoint of Base to Legs of Isosceles Triangles

Illustration to show the perpendiculars dropped from the midpoint of the base to the legs of an isosceles…

Illustration to show that the difference of the distances from any point in the base produced of an isosceles triangle to the equal sides of the triangle is constant.

Point in Base of Isosceles Triangle

Illustration to show that the difference of the distances from any point in the base produced of an…

Illustration to show the perpendiculars dropped from any point in the equilateral triangle to the three sides is constant, and equal to the altitude.

Perpendiculars Dropped Any Point in the Equilateral Triangle

Illustration to show the perpendiculars dropped from any point in the equilateral triangle to the three…

Illustration to show the bisector of the vertical angle A of a triangle ABC, and the bisectors of the exterior angles at the base formed by producing the sides AB and AC, meet in a point which is equidistant from the base and the sides produced.

Triangle With Bisectors of Vertical Angles

Illustration to show the bisector of the vertical angle A of a triangle ABC, and the bisectors of the…

Illustration to show if the bisector of the base angles of a triangle are drawn, and through their point of intersection a line is drawn parallel to the base, the length of this parallel between the sides is equal to the sum of the segments of the sides between the parallel and the base.

Triangle With Bisectors of Base Angles

Illustration to show if the bisector of the base angles of a triangle are drawn, and through their point…

Illustration to show the bisector of the vertical angle of a triangle makes with the perpendicular from the vertex to the base an angle equal to half the difference of the base angles.

Triangle With Bisector and Perpendicular From Vertex Drawn

Illustration to show the bisector of the vertical angle of a triangle makes with the perpendicular from…

Illustrations of a circle with segment, semicircle, sector, quadrant, and central angles drawn.

Circle with Segment, Semicircle, Sector, Quadrant, and Central Angle

Illustrations of a circle with segment, semicircle, sector, quadrant, and central angles drawn.

Illustrations of a circle with arc, chord, inscribed angle, and circumscribed about a polygon.

Circle with Arc, Chord, Inscribed Angle, Circumscribed Polygon

Illustrations of a circle with arc, chord, inscribed angle, and circumscribed about a polygon.

Illustration of a circle which illustrates that the tangents to a circle drawn from an external point are equal, and make equal angles with the line joining the point to the center.

Circle With Two Tangents Drawn From an External Point

Illustration of a circle which illustrates that the tangents to a circle drawn from an external point…

Illustration of equal circles to show that an inscribed angle is measured by half the arc intercepted between its sides.

Circles With Inscribed Angles

Illustration of equal circles to show that an inscribed angle is measured by half the arc intercepted…

Illustration of a circle with a right angle inscribed in a semicircle.

Circle With Inscribed Right Angle in Semicircle

Illustration of a circle with a right angle inscribed in a semicircle.

Illustration of a circle with an angle inscribed in a segment greater than a semicircle, an acute angle.

Circle With Inscribed Angle Greater Than Semicircle

Illustration of a circle with an angle inscribed in a segment greater than a semicircle, an acute angle.

Illustration of a circle with an angle inscribed in a segment less than a semicircle, an obtuse angle.

Circle With Inscribed Angle Less Than Semicircle

Illustration of a circle with an angle inscribed in a segment less than a semicircle, an obtuse angle.

Illustration of a circle with two intersecting chords within the circumference. The angle formed is measured by half the sum of the intercepted arcs.

Circle With Two Intersecting Chords

Illustration of a circle with two intersecting chords within the circumference. The angle formed is…

Illustration of a circle showing an angle included by a tangent and a chord drawn from the point of contact. The angle is measured by half the intercepted arc.

Circle With Chord and Tangent

Illustration of a circle showing an angle included by a tangent and a chord drawn from the point of…

Illustration showing angles formed by two secants, two tangents, or a tangent and a secant, drawn to a circle form an external point. The angle is measured by half the difference of the intercepted arcs.

Circles With Angles Formed by Secants and Tangents

Illustration showing angles formed by two secants, two tangents, or a tangent and a secant, drawn to…

Illustration showing arcs measured in positive and negative angles.

Positive and Negative Arcs in Circles

Illustration showing arcs measured in positive and negative angles.

Illustration showing various circles and the angles formed by intersecting lines.

Intersecting Lines in Circles

Illustration showing various circles and the angles formed by intersecting lines.

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 create an equal angle given a point in a given straight line and a given angle.

Construction of an Equal Angle Given a Point and a Straight Line

Illustration of the construction used to create an equal angle given a point in a given straight line…

Illustration of the construction used to find the third angle of a triangle when two of the angles are given.

Construction to Find the Third Angle of a Triangle When Given Two Angles

Illustration of the construction used to find the third angle of a triangle when two of the angles are…

Illustration of the construction used to make a triangle when given two sides and the included angle.

Construction of a Triangle When Given Two Sides and Included Angle

Illustration of the construction used to make a triangle when given two sides and the included angle.

Illustration of the construction used to make a triangle when given a side and two angles.

Construction of a Triangle When Given a Side and Two Angles

Illustration of the construction used to make a triangle when given a side and two angles.

Illustration of the construction used to make a triangle when given two sides and the angle opposite one of them. This is for case 1 of the ambiguous case, when a is less than b.

Construction of a Triangle When Given Two Sides and the Angle Opposite (Ambiguous Case)

Illustration of the construction used to make a triangle when given two sides and the angle opposite…

Illustration of the construction used to make a triangle when given two sides and the angle opposite one of them. This is for case 2 of the ambiguous case, when a is equal to b.

Construction of a Triangle When Given Two Sides and the Angle Opposite (Ambiguous Case)

Illustration of the construction used to make a triangle when given two sides and the angle opposite…

Illustration of the construction used to make a triangle when given two sides and the angle opposite one of them. This is for case 2 of the ambiguous case, when a is equal to b.

Construction of a Triangle When Given Two Sides and the Angle Opposite (Ambiguous Case)

Illustration of the construction used to make a triangle when given two sides and the angle opposite…

Illustration of the construction used to make a parallelogram when given two sides and the included angle.

Construction of a Parallelogram When Given Two Sides and Included Angle

Illustration of the construction used to make a parallelogram when given two sides and the included…

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…

Illustration of the construction used upon a given straight line, to describe a segment of a circle in which a given angle may be inscribed.

Construction to Describe a Segment of a Circle in Which an Angle Can Be Inscribed

Illustration of the construction used upon a given straight line, to describe a segment of a circle…

Illustration used to construct a triangle , given the perimeter, one angle, and the altitude from the vertex of the given angle.

Construction of a Triangle Given Perimeter, Angle, Altitude

Illustration used to construct a triangle , given the perimeter, one angle, and the altitude from the…

Front view of the bones of the thorax, including the ribs, sternum and vertebrae. Labels: 1, first bone of the sternum; 2, second bone of the sternum; 3, third bone or ensiform cartilage; 4, first dorsal vertebra; 5, last or twelfth dorsal vertebra; 6, first rib; 7, its head; 8, its neck; 9, its tubercle; 10, seventh or last true rib; 11, its cartilage; 12, angle of eleventh rib; 13, its body.

The Bones of the Thorax

Front view of the bones of the thorax, including the ribs, sternum and vertebrae. Labels: 1, first bone…

Venter of scapula. Labels: 1, 1, 1, oblique ridges; 2, 2, fossa for subscapularis muscle; 3, superior border; 4, superior angle; 5, suprascapular notch; 6, coracoid process; 7, acromion process; 8, spine of scapula; 9, articular surface; 10, glenoid cavity; 11, head of scapula; 12, neck; 13, interior border; 14, inferior angle; 15, posterior border; 16, origin of spine.

Scapula

Venter of scapula. Labels: 1, 1, 1, oblique ridges; 2, 2, fossa for subscapularis muscle; 3, superior…

Illustration to show that an angle bisector of a triangle divides the opposite side into segments which are proportional to the adjacent sides.

Angle Bisector of Triangle Dividing Opposite Side Into Proportionate Segments

Illustration to show that an angle bisector of a triangle divides the opposite side into segments which…

Illustration to show that a bisector of a an exterior angle of a triangle divides the opposite side into segments which are proportional to the adjacent sides.

Exterior Angle Bisector of Triangle Dividing Opposite Side Into Proportionate Segments

Illustration to show that a bisector of a an exterior angle of a triangle divides the opposite side…

A right triangle with degrees, 46, 44, 90

Right Triangle degrees, 46, 44, 90

A right triangle with degrees, 46, 44, 90

A right triangle with degrees, 47, 43, 90

Right Triangle degrees, 47, 43, 90

A right triangle with degrees, 47, 43, 90

A right triangle with degrees, 48, 42, 90

Right Triangle degrees, 48, 42, 90

A right triangle with degrees, 48, 42, 90

A right triangle with degrees, 49, 41, 90

Right Triangle degrees, 49, 41, 90

A right triangle with degrees, 49, 41, 90

A right triangle with degrees, 50, 40, 90

Right Triangle degrees, 50, 40, 90

A right triangle with degrees, 50, 40, 90

A right triangle with degrees, 51, 39, 90

Right Triangle degrees, 51, 39, 90

A right triangle with degrees, 51, 39, 90

A right triangle with degrees, 52, 38, 90

Right Triangle degrees, 52, 38, 90

A right triangle with degrees, 52, 38, 90

A right triangle with degrees, 53, 37, 90

Right Triangle degrees, 53, 37, 90

A right triangle with degrees, 53, 37, 90

A right triangle with degrees, 54, 36, 90

Right Triangle degrees, 54, 36, 90

A right triangle with degrees, 54, 36, 90

A right triangle with degrees, 55, 35, 90

Right Triangle degrees, 55, 35, 90

A right triangle with degrees, 55, 35, 90

A right triangle with degrees, 56, 34, 90

Right Triangle degrees, 56, 34, 90

A right triangle with degrees, 56, 34, 90

A right triangle with degrees, 57, 33, 90

Right Triangle degrees, 57, 33, 90

A right triangle with degrees, 57, 33, 90