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Illustration of an equilateral triangle inscribed in a closed concave geometric figure with 24 sides in the shape of a 12-point star. The two figures are concentric.

Triangle Inscribed In A 12-Point Star

Illustration of an equilateral triangle inscribed in a closed concave geometric figure with 24 sides…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts an angelfish.

Angelfish

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts an angelfish.

Angelfish

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts an angelfish.

Angelfish

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts an angelfish.

Angelfish

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

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…

Angles used to illustrate the sum and difference of two angles and trig identities.

Angles Used to Illustrate Sum and Difference of Two Angles

Angles used to illustrate the sum and difference of two angles and trig identities.

Illustration of two triangles, showing the sine of the sum of two acute angles expressed in terms of the sines and cosines of the angles.

Sum of 2 Acute Angles

Illustration of two triangles, showing the sine of the sum of two acute angles expressed in terms of…

Lines drawn to horizontal to form triangle ratios (reference triangles, angles).

Reference Angles/Triangles Formed by Angles in Quadrants

Lines drawn to horizontal to form triangle ratios (reference triangles, angles).

Lines drawn to horizontal to form triangle ratios (reference triangles, angles). Axes, quadrants, abscissa, ordinate, and distance labeled.

Reference Angles/Triangles Formed by Angles in Quadrants With Labels

Lines drawn to horizontal to form triangle ratios (reference triangles, angles). Axes, quadrants, abscissa,…

Illustration of a decagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are decagons.

Decagonal Antiprism

Illustration of a decagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a decagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are decagons.

Decagonal Antiprism

Illustration of a decagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a dodecagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are dodecagons.

Dodecagonal Antiprism

Illustration of a dodecagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a dodecagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are dodecagons.

Dodecagonal Antiprism

Illustration of a dodecagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a heptagonal, or sometimes known as a septagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are heptagons/septagons.

Heptagonal/Septagonal Antiprism

Illustration of a heptagonal, or sometimes known as a septagonal antiprism. An antiprism is formed by…

Illustration of a heptagonal, or sometimes known as a septagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are heptagons/septagons.

Heptagonal/Septagonal Antiprism

Illustration of a heptagonal, or sometimes known as a septagonal antiprism. An antiprism is formed by…

Illustration of a hexagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are hexagons.

Hexagonal Antiprism

Illustration of a hexagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a hexagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are hexagons.

Hexagonal Antiprism

Illustration of a hexagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a nonagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are nonagons.

Nonagonal Antiprism

Illustration of a nonagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a nonagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are nonagons.

Nonagonal Antiprism

Illustration of a nonagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of an octagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are octagons.

Octagonal Antiprism

Illustration of an octagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of an octagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are octagons.

Octagonal Antiprism

Illustration of an octagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are pentagons.

Pentagonal Antiprism

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are pentagons.

Pentagonal Antiprism

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are pentagons.

Pentagonal Antiprism

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are pentagons.

Pentagonal Antiprism

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a skewed (non-right) heptagonal, or sometimes known as a septagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are heptagons/septagons.

Skewed Heptagonal/Septagonal Antiprism

Illustration of a skewed (non-right) heptagonal, or sometimes known as a septagonal antiprism. An antiprism…

Illustration of a skewed (non-right) hexagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are hexagons.

Skewed Hexagonal Antiprism

Illustration of a skewed (non-right) hexagonal antiprism. An antiprism is formed by having two parallel…

Illustration of a skewed (non-right) nonagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are nonagons.

Skewed Nonagonal Antiprism

Illustration of a skewed (non-right) nonagonal antiprism. An antiprism is formed by having two parallel…

Illustration of a skewed (non-right) octagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are octagons.

Skewed Octagonal Antiprism

Illustration of a skewed (non-right) octagonal antiprism. An antiprism is formed by having two parallel…

Illustration of a skewed (non-right) pentagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are pentagons.

Skewed Pentagonal Antiprism

Illustration of a skewed (non-right) pentagonal antiprism. An antiprism is formed by having two parallel…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts an arch.

Arch

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts an arch.

Arch

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts an arch.

Arch

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts an arch.

Arch

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

"In the triangle above, the line AB is its altitude. Since we know how to find the area of one triangle, we can find the areas of as many triangles as we have made from our circle. Therefore, to find the area of a circle: Find the area of one of the triangles and multiply by the number of triangles." -Foster, 1921

Area of Circle with Triangles

"In the triangle above, the line AB is its altitude. Since we know how to find the area of one triangle,…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts an arrow pointing left.

Arrow Pointing Left

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts an arrow pointing left.

Arrow Pointing Left

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts an arrow pointing left.

Arrow Pointing Left

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts an arrow pointing left.

Arrow Pointing Left

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a bear.

Bear

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a bear.

Bear

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a bear.

Bear

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a bear.

Bear

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a bearded man in a tophat.

Bearded Man in a Tophat

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a bearded man in a tophat.

Bearded Man in a Tophat

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a bearded man in tophat.

Bearded Man in Tophat

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a bearded man in tophat.

Bearded Man in Tophat

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a beta fish.

Beta Fish

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a beta fish.

Beta Fish

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a beta fish.

Beta Fish

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a beta fish.

Beta Fish

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a boat.

Boat

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a boat.

Boat

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a boat.

Boat

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a boat.

Boat

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a camel.

Camel

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a camel.

Camel

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a camel.

Camel

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…