ClipArt ETC
2/3 of a 3 sided polygon

Fractions of 3-sided Polygon

2/3 of a 3 sided polygon

3/3 of a 3 sided polygon

Fractions of 3-sided Polygon

3/3 of a 3 sided polygon

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 a triangle with an interior segment drawn

Triangle With Interior Segment

Illustration showing a triangle with an interior segment drawn

Illustration showing a triangle with an exterior segment drawn to show and exterior angle. This can be shown to show adjacent angles ACB and ACD as well.

Triangle With Segment Extended for Exterior Angle

Illustration showing a triangle with an exterior segment drawn to show and exterior angle. This can…

Illustration showing a scalene triangle (one that has no two sides equal).

Scalene Triangle

Illustration showing a scalene triangle (one that has no two sides equal).

Illustration showing an isosceles triangle (one that has two sides equal).

Isosceles Triangle

Illustration showing an isosceles triangle (one that has two sides equal).

Illustration showing an equilateral triangle (one that has three sides equal).

Equilateral Triangle

Illustration showing an equilateral triangle (one that has three sides equal).

Illustration showing a right triangle (one that has one right angle).

Right Triangle

Illustration showing a right triangle (one that has one right angle).

Illustration showing an obtuse triangle (one that has one obtuse angle).

Obtuse Triangle

Illustration showing an obtuse triangle (one that has one obtuse angle).

Illustration showing an acute triangle (one that has all three angles that are acute).

Acute Triangle

Illustration showing an acute triangle (one that has all three angles that are acute).

Illustration showing an equiangular triangle (one that has all three angles that are equal).

Equiangular Triangle

Illustration showing an equiangular triangle (one that has all three angles that are equal).

Illustration showing a triangle with exterior angles. This can be used to show the sum of the three angles of a triangle is equal to two right angles.

Triangle with Exterior Angles Drawn

Illustration showing a triangle with exterior angles. This can be used to show the sum of the three…

Illustration showing a triangle with angles A, B, and C labeled.

Triangle ABC

Illustration showing a triangle with angles A, B, and C labeled.

Illustration showing two equal triangles.

Equal Triangles

Illustration showing two equal triangles.

Illustration showing an isosceles triangle with a segment inside. This can be used to show that in an isosceles triangle the angles opposite the equal sides are equal.

Isosceles Triangle With Interior Segment Drawn

Illustration showing an isosceles triangle with a segment inside. This can be used to show that in an…

Illustration showing two equal triangles. This can be used to show that two triangles are equal if the three sides of the one are equal, respectively, to the three sides of the other.

Equal Triangles by Side Side Side

Illustration showing two equal triangles. This can be used to show that two triangles are equal if the…

Illustration showing two equal right triangles. This can be used to show that two right triangles are equal if a leg and the hypotenuse of the one are equal, respectively, to a leg and the hypotenuse of the other.

Equal Right Triangles by Hypotenuse Leg

Illustration showing two equal right triangles. This can be used to show that two right triangles are…

Illustration showing a triangle with a segment inside.

Triangle With Interior Segment Drawn

Illustration showing a triangle with a segment inside.

Illustration showing three triangles. This is used to show the following theorem: If two triangles have two sides of the one equal, respectively, to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Three Triangles Used to Compare Sides

Illustration showing three triangles. This is used to show the following theorem: If two triangles have…

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 of a triangle with the median drawn.

Triangle With Median Drawn

Illustration of a triangle with the median drawn.

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.