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Everyone knows what a triangle is, yet very few people appreciate that the common three-sided figure holds many intriguing secrets. For example, if a circle is inscribed in any random triangle and then three lines are drawn from the three points of tangency to the opposite vertices of the triangle, these lines will always meet at a common point--no matter what the shape of the triangle. This and many more interesting geometrical properties are revealed...
Description
In this video we'll learn how to solve for unknown values in two similar triangles. Similar triangles are triangles that have the same three interior angles, but different side lengths. If two triangles have the same three interior angles, then we can set up a proportion between their side lengths.
Description
In this video we'll learn how to use the midsegment of a triangle to establish a relationship between the smaller, interior triangle, and the larger, exterior triangle. When a line segment has its endpoints on opposite sides of the triangle, and it's parallel to the base of the triangle, we can set up a proportion between the side lengths.
Description
In this video we'll learn how to use the SSS (side-side-side), SAS (side-angle-side), and AA (angle-angle) theorems to prove that two triangles are similar. Similar triangles are triangles that have three congruent interior angle measures. They may have different side lengths, or they may be rotated or flipped, but their three interior angles are the same.
10) Triangles
Description
Covers equilateral, isosceles, right, congruent, and similar triangles; provides examples from architecture (the Bank of China Tower, with a triangular base to help the Hong Kong skyscraper withstand typhoon winds and the Eiffel Tower in Paris). Looks at why triangles are better architectural support than rectangles or other shapes. Reveals also, why ancient merchant ships were able to go farther and faster with triangular sails, the same principle...
Description
In this video we'll learn how to use the pythagorean theorem, which is a theorem that applies only to right-triangles (triangles that include a 90-degree angle). The pythagorean theorem tells us that the sum of the squares of the lengths of the legs is equal to the sum of the length of the hypotenuse (the longest side).
Description
In this video we'll learn about the special things that happen in the specific instance of a 45-45-90 triangle, which is a triangle whose three interior angles are 45 degrees, 45 degrees, and 90 degrees. This triangle, by definition, is an isosceles triangle, and it's one half of a square, split on the square's diagonal.
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