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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 torch.

Torch

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

Illustration of a leaning tower with a perpendicular drawn from the top of the tower to the ground to form a right triangle.

Leaning Tower

Illustration of a leaning tower with a perpendicular drawn from the top of the tower to the ground to…

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 tree.

Tree

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 tree.

Tree

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 tree.

Tree

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 tree.

Tree

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

Illustration of a palm tree that is perpendicular to the ground. The tree is perfectly straight, as is the ground. This drawing could be used for shadow, proportion, trigonometric, or Pythagorean Theorem problems.

Palm Tree Perpendicular to Ground

Illustration of a palm tree that is perpendicular to the ground. The tree is perfectly straight, as…

A cylindrical steel bar, bent into a equilateral triangle. It is struck with a small bar of the same metal.

Triangle

A cylindrical steel bar, bent into a equilateral triangle. It is struck with a small bar of the same…

A bar of steel bent into the form of a triangle, and struck with a small rod.

Triangle

A bar of steel bent into the form of a triangle, and struck with a small rod.

Triangle with sides a, b, c and angles A, B, C labeled.

Triangle

Triangle with sides a, b, c and angles A, B, C labeled.

Triangle with sides labeled with numerals 28, 36, 40 and angles A, B, C labeled.

Triangle 28, 36, 40

Triangle with sides labeled with numerals 28, 36, 40 and angles A, B, C labeled.

Triangle with labels A, B, C, D

Triangle

Triangle with labels A, B, C, D

Triangle with segments drawn.

Triangle With Segments

Triangle with segments drawn.

Triangle with height/altitude h and median m.

Triangle With Height and Median

Triangle with height/altitude h and median m.

An illustration of a triangle comprised of a church and two lines. This illustration can be used to determine the height of the church steeple, the hypotenuse, and distance of the tower from object one and two.

Triangle with Church

An illustration of a triangle comprised of a church and two lines. This illustration can be used to…

Illustration used to construct a triangle given the length of the base and the two base angles.

Construction of Triangle Given Angles and Base

Illustration used to construct a triangle given the length of the base and the two base angles.

An illustration of a three triangles created with boats and a lighthouse. This is an example illustration used to fine the height of an object situated about the plane of observation, and its height above the plane.

Triangle with Lighthouse

An illustration of a three triangles created with boats and a lighthouse. This is an example illustration…

Square with dotted lines that are lines of symmetry.

Lines of Symmetry, Triangle With

Square with dotted lines that are lines of symmetry.

An illustration of a triangle comprised of a tower and two lines. This illustration can be used to determine the height of the tower, the hypotenuse, and distance of the tower from the object.

Triangle with Tower

An illustration of a triangle comprised of a tower and two lines. This illustration can be used to determine…

An illustration of a triangle comprised of a tree and two lines. This is an example of a problem that can be used to fine the distance of an inaccessible object without measuring elevation and whether on a horizontal plane or not.

Triangle with Tree

An illustration of a triangle comprised of a tree and two lines. This is an example of a problem that…

30-60-90 Right Triangle

Triangle 30-60-90

30-60-90 Right Triangle

30-60-90 right triangle.

30-60-90 Right Triangle

30-60-90 right triangle.

37-49-94 Triangle

Triangle 37-49-94

37-49-94 Triangle

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 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 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 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 showing the three angle bisectors in a triangle.

Angle Bisectors In A Triangle

Illustration showing the three angle bisectors in a triangle.

Parallelogram illustration to show where the area of a triangle formula comes from.

Area of Triangle

Parallelogram illustration to show where the area of a triangle formula comes from.

Illustration of triangle ABC with altitude a and base b to be used to demonstrate that the area is 1/2ba.

Area of a Triangle

Illustration of triangle ABC with altitude a and base b to be used to demonstrate that the area is 1/2ba.

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 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 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 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 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 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.

Triangle construction when given two angles and the included side.

Triangle Construction When Given 2 Angles and Included Side

Triangle construction when given two angles and the included side.

Illustration used to circumscribe a circle about a given triangle.

Construction Used to Circumscribe a Circle About a Triangle

Illustration used to circumscribe a circle about a given triangle.

Illustration used to escribe a circle to a given triangle. "A circle which is tangent to one side of a triangle and to the the other two sides prolonged is said to be escribed to the triangle."

Construction Used to Escribe a Circle to a Triangle

Illustration used to escribe a circle to a given triangle. "A circle which is tangent to one side of…

Illustration used to inscribe a circle in a given triangle.

Construction Used to Inscribe a Circle in a Triangle

Illustration used to inscribe a circle in a given triangle.

Illustration showing intersecting straight lines meeting to form a triangle. It is formed by the intersection of the surface of a cone with a plane parallel to the axis and actually containing the axis.

Degenerate Conic Forming Triangle

Illustration showing intersecting straight lines meeting to form a triangle. It is formed by the intersection…

Triangle with dimensions labeled. Triangle can be used to calculate area.

Triangle With Dimensions

Triangle with dimensions labeled. Triangle can be used to calculate area.

Triangle with dimensions labeled. Triangle can be used to calculate area.

Triangle With Dimensions

Triangle with dimensions labeled. Triangle can be used to calculate area.

Mechanical drawing triangle.

Drawing Triangle

Mechanical drawing triangle.

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).

"Having equal sides." — Williams, 1889

Equilateral triangle

"Having equal sides." — Williams, 1889

Sketch of equilateral triangle with bisectors, medians, and altitudes.

Equilateral Triangle

Sketch of equilateral triangle with bisectors, medians, and altitudes.

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

Equilateral Triangle

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

An illustration showing a triangle with interior angles A, B, C, and exterior angles D, and A' + B'.

Exterior And Interior Angles Of A Triangle

An illustration showing a triangle with interior angles A, B, C, and exterior angles D, and A' + B'.

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 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.

Sketch of isosceles triangle with labels.

Isosceles Triangle

Sketch of isosceles triangle with labels.

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

Isosceles Triangle

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

Isosceles right triangle.

Isosceles Right Triangle

Isosceles right triangle.

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 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 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 of a triangle with the median drawn.

Triangle With Median Drawn

Illustration of a triangle with the median drawn.

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 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…