Groups of change with totals from 1 to 100 cents using the least amount of coins.

98 Cents

Groups of change with totals from 1 to 100 cents using the least amount of coins.

Groups of change with totals from 1 to 100 cents using the least amount of coins.

99 Cents

Groups of change with totals from 1 to 100 cents using the least amount of coins.

Groups of change with totals from 1 to 100 cents using the least amount of coins.

100 Cents

Groups of change with totals from 1 to 100 cents using the least amount of coins.

An illustration of a straight line with 5 points dividing it into 4 equal parts. Multiple of a given line.

Straight Line With Points Divided Into Equal Parts

An illustration of a straight line with 5 points dividing it into 4 equal parts. Multiple of a given…

An illustration showing when one straight line meets another straight line and makes the adjacent angles equal, each of these angles is called a right angle.

Right Angles With Same Vertex

An illustration showing when one straight line meets another straight line and makes the adjacent angles…

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 that if two parallel lines are cut by a transversal, then the alternate interior angles are equal.

Parallel Lines Cut By A Transversal

Illustration showing that if two parallel lines are cut by a transversal, then the alternate interior…

Illustration showing that when two straight lines in the same plane are cut by a transversal, if the alternate interior angles are equal, the two straight lines are parallel.

Parallel Lines Cut By A Transversal

Illustration showing that when two straight lines in the same plane are cut by a transversal, if the…

Illustration showing that when two parallel lines are cut by a transversal, the exterior-interior angles are equal.

Parallel Lines Cut By A Transversal

Illustration showing that when two parallel lines are cut by a transversal, the exterior-interior angles…

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 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 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 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 square, a rectangle with all sides equal.

Square

Illustration of a square, a rectangle with all sides equal.

Illustration of a rhombus, which is a rhomboid with all sides equal.

Rhombus

Illustration of a rhombus, which is a rhomboid with all sides equal.

Illustration of two angles whose sides are parallel, each to each, to show they are either equal or supplementary.

Angles With Parallel Sides

Illustration of two angles whose sides are parallel, each to each, to show they are either equal or…

Illustration of two parallel lines with equal segments between them. Two parallel lines are everywhere equally distant.

Parallel Lines With Equal Segments Between

Illustration of two parallel lines with equal segments between them. Two parallel lines are everywhere…

Illustration of a two equal parallelograms. Two parallelograms are equal, if two sides and the included angle of the one are equal, respectively, to two sides and the included angle of the other.

Equal Parallelograms

Illustration of a two equal parallelograms. Two parallelograms are equal, if two sides and the included…

Illustration showing that when three or more parallel lines intercept equal parts on one transversal, they intercept equal parts on every transversal.

Parallel Lines Cut By A Transversal

Illustration showing that when three or more parallel lines intercept equal parts on one transversal,…

Illustration of a trapezoid, with the median drawn. The median of a trapezoid is parallel to the bases, and is equal to half the sum of the bases.

Trapezoid With Median

Illustration of a trapezoid, with the median drawn. The median of a trapezoid is parallel to the bases,…

Illustration of a two polygons. Polygons may be mutually equiangular without being mutually equilateral.

Equiangular Polygons

Illustration of a two polygons. Polygons may be mutually equiangular without being mutually equilateral.

Illustration of two polygons. Polygons may be mutually equilateral without being mutually equiangular (except for triangles).

Equilateral Polygons

Illustration of two polygons. Polygons may be mutually equilateral without being mutually equiangular…

Illustration of a quadrilateral which has two adjacent sides equal and the other two sides equal. It is symmetrical with respect to the diagonal joining the vertices of the angles formed by the equal sides, and the diagonals are perpendicular to each other.

Quadrilateral with Symmetry

Illustration of a quadrilateral which has two adjacent sides equal and the other two sides equal. It…

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 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 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 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 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 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…

Illustration to show that if the diagonals of a parallelogram are equal, the figure is a rectangle.

Rectangle With Diagonals

Illustration to show that if the diagonals of a parallelogram are equal, the figure is a rectangle.

Illustrations of an isosceles trapezoid with equal diagonals drawn.

Isosceles Trapezoid With Equal Diagonals

Illustrations of an isosceles trapezoid with equal diagonals drawn.

Illustrations of a square with diagonal DB, BE cut off equal to BC, and EF drawn perpendicular to BD meeting DC at F. DE is equal to EF and to FC.

Square With Diagonal

Illustrations of a square with diagonal DB, BE cut off equal to BC, and EF drawn perpendicular to BD…

Illustrations of 2 equal circles with radii drawn.

Equal Circles With Radii

Illustrations of 2 equal circles with radii drawn.

Illustrations of 2 equal circles with radii drawn.

Equal Circles With Radii and Chords

Illustrations of 2 equal circles with radii drawn.

Illustration of a circle with equal chords, which are equally distant from the center.

Circle With Equal Chords

Illustration of a circle with equal chords, which are equally distant from the center.

Illustration of a circle with unequal chords, which are unequally distant from the center.

Circle With Unequal Chords

Illustration of a circle with unequal chords, which are unequally distant from the center.

Illustration of a circle with parallels intercepting equal arcs on a circumference.

Circles With Parallels Intercepting Equal Arcs

Illustration of a circle with parallels intercepting equal arcs on a circumference.

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 two central angles have the same ratio as their intercepted arcs.

Equal Circles With Intercepted Arcs

Illustration of equal circles to show that two central angles have the same ratio as their intercepted…

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 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 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 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 divide a straight line into a given number of equal parts.

Construction of a Straight Line Divided Into Equal Parts

Illustration of the construction used to divide a straight line into a given number of equal parts.

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…

A flashcard featuring a math symbol for Approximately Equal To

Flashcard of a math symbol for Approximately Equal To

A flashcard featuring a math symbol for Approximately Equal To

A flashcard featuring an illustration of a Polygon with ten equal sides

Flashcard of a Polygon with ten equal sides

A flashcard featuring an illustration of a Polygon with ten equal sides

A flashcard featuring an illustration of a polygon with twelve equal sides

Flashcard of a polygon with twelve equal sides

A flashcard featuring an illustration of a polygon with twelve equal sides

A flashcard featuring an illustration of a polygon with nine equal sides

Flashcard of a polygon with nine equal sides

A flashcard featuring an illustration of a polygon with nine equal sides

A flashcard featuring a math symbol for Equal To

Flashcard of a math symbol for Equal To

A flashcard featuring a math symbol for Equal To