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Chapter 3: Polygons and Their Relations

If one side of a triangle is longer than another side, then the measure of the angles opposite the longer side is greater than the measure of the angle opposite the shorter side.

If one angle of a triangle has a greater measure than a second angle, then the side opposite the greater angle is longer than the side opposite the smaller angle.

In a scalene triangle, the longest side is opposite the largest angle and the largest angle is opposite the longest side.

The perpendicular segment from a point to a line is the shortest segment from the point to the line.

The longer side of a right triangle is the hypotenuse.

# Right Triangles

Right triangles are a special kind of triangle that has two acute angles and one 90 degree angle. They have two legs that are opposite the two acute angles and one hypotenuse that is opposite the 90 degree angle. Right triangles are very important because many advanced math topics involve the uses of right triangles. Here are some most common properties of right triangles:

In a right triangle, the altitude to the hypotenuse forms two similar right triangles, each of which is also similar to the original triangle.

In a right triangle, the square of the length of the altitude to the hypotenuse equals the product of the lengths of the segments formed on the hypotenuse.

If the altitude is drawn to the hypotenuse of a right triangle, then the square of the length of either leg equals the product of the lengths of the hypotenuse and the segment of the hypotenuse adjacent to that leg.

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