Illustration of a triangle with a segment parallel to the base.

Triangle With Parallel Segment Drawn

Illustration of a triangle with a segment parallel to the base.

Illustration of a right triangle with the midpoint of the hypotenuse drawn.

Right Triangle With Midpoint of Hypotenuse Drawn

Illustration of a right triangle with the midpoint of the hypotenuse drawn.

Illustration of a right triangle with one angle the double of the other.

Right Triangle With One Angle Double the Other

Illustration of a right triangle with one angle the double of the other.

Illustration to show if two triangles have two sides of the one equal, respectively, to two sides of the other, and the angles opposite two equal sides equal, the angles opposite the other two equal sides are equal or supplementary, and if equal the triangles are equal.

Proof of Equal Triangles Drawing

Illustration to show if two triangles have two sides of the one equal, respectively, to two sides of…

Illustration to show angle bisectors in a triangle. It is known as the incenter.

Incenter of Triangle

Illustration to show angle bisectors in a triangle. It is known as the incenter.

Illustration to show perpendicular bisectors in a triangle. It is known as the circumcenter.

Circumcenter of Triangle

Illustration to show perpendicular bisectors in a triangle. It is known as the circumcenter.

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 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 two triangles with the same base and on the same side of the base.

Triangles With The Same Base

Illustration to show two triangles with the same base and on the same side of the base.

Illustration to show lines drawn from the vertices to join at a point within the triangle.

Triangle With Lines From the Vertices That Join a Point Within

Illustration to show lines drawn from the vertices to join at a point within the triangle.

Illustration to show that if from any point in the base of an isosceles triangle parallels to the legs are drawn, a parallelogram is formed whose perimeter is constant, being equal to the sum of the legs of the triangle.

Isosceles Triangle With Parallelogram inside

Illustration to show that if from any point in the base of an isosceles triangle parallels to the legs…

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 a chord and triangle inside.

Circle with Chord and Triangle

Illustrations of a circle with a chord and triangle inside.

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 showing a circle with a diameter, radius, lines, triangle, and segment drawn.

Circle With Diameter, Radius, Segment, Line

Illustration showing a circle with a diameter, radius, lines, triangle, and segment drawn.

Illustration showing 2 intersecting circles with a lines drawn that form a triangle.

Two Intersecting Circles With Lines

Illustration showing 2 intersecting circles with a lines drawn that form a triangle.

Illustration showing the diameter of a circle inscribed in a right triangle is equal to the difference between the sum of the legs and the hypotenuse.

Circle Inscribed in a Right Triangle

Illustration showing the diameter of a circle inscribed in a right triangle is equal to the difference…

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 showing an equilateral triangle inscribed in a circle.

Circle With Inscribed Equilateral Triangle

Illustration showing an equilateral triangle inscribed in a circle.

Illustration showing a circle with an inscribed quadrilateral and triangles formed by extended chords.

Circle With Inscribed Quadrilateral and Triangles Formed

Illustration showing a circle with an inscribed quadrilateral and triangles formed by extended chords.

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 triangle when given three sides.

Construction of a Triangle When Given Three Sides

Illustration of the construction used to make a triangle when given three sides.

Illustration of the construction used to circumscribe a circle about a given triangle.

Construction to Circumscribe a Circle About a Triangle

Illustration of the construction used to circumscribe a circle about a given triangle.

Illustration of the construction used to inscribe a circle in a given triangle.

Construction to Inscribe a Circle in a Triangle

Illustration of the construction used to inscribe a circle in a given triangle.

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 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…

Illustration showing a triangle with a line parallel to the base and two intersecting lines.

Triangle With Line Parallel to Base and Two Intersecting Lines

Illustration showing a triangle with a line parallel to the base and two intersecting lines.

Illustration showing a circle with an inscribed triangle and radii.

Circle With Inscribed Triangle and Radii

Illustration showing a circle with an inscribed triangle and radii.

Illustration showing a triangle with an altitude CD passing through the middle of EF. Triangles AEC and BFC are isosceles.

Triangle With Altitude and Isosceles Triangles Within

Illustration showing a triangle with an altitude CD passing through the middle of EF. Triangles AEC…

Illustration showing a circle with equilateral triangles and another circle within.

Circle With Triangles and Circle Within

Illustration showing a circle with equilateral triangles and another circle within.

Illustration to show that if a line is drawn through two sides of a triangle parallel to the third side, it divides those sides proportionally.

Triangle Divided by Parallel Lines to Form Proportionate Triangles

Illustration to show that if a line is drawn through two sides of a triangle parallel to the third side,…

Illustration to show that if a line divides two sides of a triangle proportionally, it is parallel to the third side.

Triangle Divided by Parallel Lines to Form Proportionate Triangles

Illustration to show that if a line divides two sides of a triangle proportionally, it is parallel to…

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…

One large triangle for pattern block set.

Large Triangle for Pattern Block Set

One large triangle for pattern block set.

Six large triangles for pattern block set.

Large Triangles for Pattern Block Set

Six large triangles for pattern block set.

Six large triangles for pattern block set.

Large Triangles for Pattern Block Set

Six large triangles for pattern block set.

Nine large triangles for pattern block set.

Large Triangles for Pattern Block Set

Nine large triangles for pattern block set.

Forty-two small triangles for pattern block set.

Small Triangles for Pattern Block Set

Forty-two small triangles for pattern block set.

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…