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Diagram used to prove the theorem: "In a spherical triangle, the greater side is opposite the greater angle, and conversely."

Side Comparison of Spherical Triangle

Diagram used to prove the theorem: "In a spherical triangle, the greater side is opposite the greater…

Square with diagonal and angles labeled.

Square

Square with diagonal and angles labeled.

An illustration of a square and triangles within the square. This is an example of a problem that can be used to fine the distances of two inaccessible objects without measuring elevation and whether on a horizontal plane or not.

Square

An illustration of a square and triangles within the square. This is an example of a problem that can…

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 the St. Petersburg Pier.

St. Petersburg Pier

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 the St. Petersburg Pier.

St. Petersburg Pier

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 the St. Petersburg Pier.

St. Petersburg Pier

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 the St. Petersburg Pier.

St. Petersburg Pier

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 standing fox.

Standing Fox

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 standing fox.

Standing Fox

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 standing fox.

Standing Fox

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 standing fox.

Standing Fox

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 stingray.

Stingray

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 stingray.

Stingray

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 stingray.

Stingray

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 stingray.

Stingray

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

"An exercise in starting and stopping short lines. Draw three-inch square. Draw diagonals with 45-degree triangle. With scale lay off 3/8" spaces along the diagonals, from their intersection. With 45-degree triangle complete figure, finishing one-quarter at a time." —French, 1911

Drawing Street Paving Intersection

"An exercise in starting and stopping short lines. Draw three-inch square. Draw diagonals with 45-degree…

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 stylized rabbit.

Stylized Rabbit

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 stylized rabbit.

Stylized Rabbit

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 stylized rabbit.

Stylized Rabbit

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 stylized rabbit.

Stylized Rabbit

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

Illustration showing a survey on the lake front in Chicago with distances and angle measures shown.

Survey of Lake Front in Chicago

Illustration showing a survey on the lake front in Chicago with distances and angle measures shown.

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 swan.

Swan

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 swan.

Swan

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 swan.

Swan

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 swan.

Swan

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 swimmer.

Swimmer

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 swimmer.

Swimmer

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 swimmer.

Swimmer

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 swimmer.

Swimmer

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

"On base AB, 3 1/2" long construct an equilateral triangle, using the 60-degree triangle. Bisect the angles with the 30-degree angle, extending the bisectors to the opposite sides. With these middle points of the sides as centers and radius equal to 1/2 the side, draw arcs cutting the bisectors. These intersection will be centers for the inscribed circles. With centers on the intersection of these circles and the bisectors, round off the points of the triangle as shown." —French, 1911

Drawing Tangent Circles and Lines with Compass and Triangles

"On base AB, 3 1/2" long construct an equilateral triangle, using the 60-degree triangle. Bisect the…

Draftsman's method to draw a tangent, AB, to a circle

Tangent To A Circle

Draftsman's method to draw a tangent, AB, to a circle

Outlines of animals (bear, kangaroo, camel, giraffe) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Animals Outline Tangram Card

Outlines of animals (bear, kangaroo, camel, giraffe) made from tangram pieces. Tangrams, invented by…

Outlines of animals (fox, rabbit, cat) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Animals Outline Tangram Card #2

Outlines of animals (fox, rabbit, cat) made from tangram pieces. Tangrams, invented by the Chinese,…

Solutions for outlines of animals (bear, kangaroo, camel, giraffe) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Animals Outline Solution Tangram Card

Solutions for outlines of animals (bear, kangaroo, camel, giraffe) made from tangram pieces. Tangrams,…

Solutions for outlines of animals (fox, rabbit, cat) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Animals Outline Solution Tangram Card #2

Solutions for outlines of animals (fox, rabbit, cat) made from tangram pieces. Tangrams, invented by…

Silhouette outlines of animals (bear, kangaroo, camel, giraffe) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Animals Silhouette Tangram Card

Silhouette outlines of animals (bear, kangaroo, camel, giraffe) made from tangram pieces. Tangrams,…

Silhouette outlines of animals (fox, rabbit, cat) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Animals Silhouette Tangram Card #2

Silhouette outlines of animals (fox, rabbit, cat) made from tangram pieces. Tangrams, invented by the…

Solutions for silhouette outlines of animals (bear, kangaroo, camel, giraffe) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Animals Silhouette Solution Tangram Card

Solutions for silhouette outlines of animals (bear, kangaroo, camel, giraffe) made from tangram pieces.…

Solutions for silhouette outlines of animals (fox, rabbit, cat) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Animals Silhouette Solution Tangram Card #2

Solutions for silhouette outlines of animals (fox, rabbit, cat) made from tangram pieces. Tangrams,…

Outlines of birds (duck, swan, turkey vulture, cormorant, and egret) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Birds Outline Tangram Card

Outlines of birds (duck, swan, turkey vulture, cormorant, and egret) made from tangram pieces. Tangrams,…

Solutions for outlines of birds (duck, swan, turkey vulture, cormorant, and egret) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Birds Outline Solution Tangram Card

Solutions for outlines of birds (duck, swan, turkey vulture, cormorant, and egret) made from tangram…

Silhouette outlines of birds (duck, swan, turkey vulture, cormorant, and egret) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Birds Silhouette Tangram Card

Silhouette outlines of birds (duck, swan, turkey vulture, cormorant, and egret) made from tangram pieces.…

Solutions for silhouette outlines of birds (duck, swan, turkey vulture, cormorant, and egret) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Birds Silhouette Solution Tangram Card

Solutions for silhouette outlines of birds (duck, swan, turkey vulture, cormorant, and egret) made from…

Outlines of boats (sailboat, ship, yacht) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Boats Outline Tangram Card

Outlines of boats (sailboat, ship, yacht) made from tangram pieces. Tangrams, invented by the Chinese,…

Solutions for outlines of boats (sailboat, ship, yacht) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Boats Outline Solution Tangram Card

Solutions for outlines of boats (sailboat, ship, yacht) made from tangram pieces. Tangrams, invented…

Silhouette outlines of boats (sailboat, ship, yacht) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Boats Silhouette Tangram Card

Silhouette outlines of boats (sailboat, ship, yacht) made from tangram pieces. Tangrams, invented by…

Solutions for silhouette outlines of boats (sailboat, ship, yacht) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Boats Silhouette Solution Tangram Card

Solutions for silhouette outlines of boats (sailboat, ship, yacht) made from tangram pieces. Tangrams,…

Outlines of buildings (house, lighthouse) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Buildings Outline Tangram Card

Outlines of buildings (house, lighthouse) made from tangram pieces. Tangrams, invented by the Chinese,…

Solutions for outlines of buildings (house, lighthouse) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Buildings Outline Solution Tangram Card

Solutions for outlines of buildings (house, lighthouse) made from tangram pieces. Tangrams, invented…

Silhouette outlines of buildings (house, lighthouse) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Buildings Silhouette Tangram Card

Silhouette outlines of buildings (house, lighthouse) made from tangram pieces. Tangrams, invented by…

Solutions for silhouette outlines of buildings (house, lighthouse) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Buildings Silhouette Solution Tangram Card

Solutions for silhouette outlines of buildings (house, lighthouse) made from tangram pieces. Tangrams,…

Outlines of fish (shark, parrot fish, angelfish, flounder, hogfish, beta) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Fish Outline Tangram Card

Outlines of fish (shark, parrot fish, angelfish, flounder, hogfish, beta) made from tangram pieces.…

Solutions for outlines of fish (shark, parrot fish, angelfish, flounder, hogfish, beta) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Fish Outline Solution Tangram Card

Solutions for outlines of fish (shark, parrot fish, angelfish, flounder, hogfish, beta) made from tangram…

Silhouette outlines of fish (shark, parrot fish, angelfish, flounder, hogfish, beta) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Fish Silhouette Tangram Card

Silhouette outlines of fish (shark, parrot fish, angelfish, flounder, hogfish, beta) made from tangram…

Solutions for silhouette outlines of fish (shark, parrot fish, angelfish, flounder, hogfish, beta) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Fish Silhouette Solution Tangram Card

Solutions for silhouette outlines of fish (shark, parrot fish, angelfish, flounder, hogfish, beta) made…

Solutions for silhouette outlines of Florida birds (seagull, mocking bird, egret, flamingo, turkey vulture, cormorant) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Florida Birds Silhouette Solution Tangram Card

Solutions for silhouette outlines of Florida birds (seagull, mocking bird, egret, flamingo, turkey vulture,…

Outlines of Florida birds (seagull, mocking bird, egret, flamingo, turkey vulture, cormorant) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Florida Birds Outline Tangram Card

Outlines of Florida birds (seagull, mocking bird, egret, flamingo, turkey vulture, cormorant) made from…

Solutions for outlines of Florida birds (seagull, mocking bird, egret, flamingo, turkey vulture, cormorant) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Florida Birds Outline Solution Tangram Card

Solutions for outlines of Florida birds (seagull, mocking bird, egret, flamingo, turkey vulture, cormorant)…

Silhouette outlines of Florida birds (seagull, mocking bird, egret, flamingo, turkey vulture, cormorant) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Florida Birds Silhouette Tangram Card

Silhouette outlines of Florida birds (seagull, mocking bird, egret, flamingo, turkey vulture, cormorant)…

Outlines of household items (iron, pipe, kettle, cup, candle, hammer) made from tangram pieces. Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. 7 figures consisting of triangles, squares, and parallelograms are used to construct the given shapes.

Household Items Outline Tangram Card

Outlines of household items (iron, pipe, kettle, cup, candle, hammer) made from tangram pieces. Tangrams,…