Geometry

Prove that a line that divides two sides of a triangle proportionally is parallel to the third side. Be sure to create a name the appropriate geometric figures.

Paul walks 25 feet away from his house and places a mirror on the ground. He backs 5 feet away from the mirror so that he can see the tip of the roof. Paul's eyes are 6 feet above the ground. Paul and the house are both perpendicular to the ground. The angles between the top of the house, the mirror, and the ground and between Paul's eyes, the mirror and the ground are congruent. What is the height of the house? Show your work and explain in complete sentences please.

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  1. Can someone please help me!!???????????

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  2. The first problem is discussed here:

    http://www.algebra.com/algebra/homework/Triangles/The-line-segment-joining-the-midpoints-of-two-sides-of-a-triangle.lesson

    Google is your friend. Most problems posted here have been discussed many times on the web.

    For #2, if you draw a diagram, you can clearly see that the two triangles with common vertex at the mirror, and top vertices at Paul's head and the top of the house, are similar, since they are both right triangles, and have congruent base angles.

    So, since Paul is 5 ft from the mirror, and the house is 25 feet from the mirrot, the house is 5 times as tall as Paul.

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