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=Similar Triangle Problems= **__Problem 1:__**In the triangle ABC shown below, A'C' is parallel to AC. Find the length y of BC' and the length x of A'A.



**__Problem 2:__** A research team wishes to determine the altitude of a mountain as follows: They use a light source at L, mounted on a structure of height 2 meters, to shine a beam of light through the top of a pole P' through the top of the mountain M'. The height of the pole is 20 meters. The distance between the altitude of the mountain and the pole is 1000 meters. The distance between the pole and the laser is 10 meters. We assume that the light source mount, the pole and the altitude of the mountain are in the same plane. Find the altitude h of the mountain.

**__Problem 3:__** The two triangles are similar and the ratio of the lengths of their sides is equal to k: AB / A'B' = BC / B'C' = CA / C'A' = k. Find the ratio BH / B'H' of the lengths of the altitudes of the two triangles.



**__Problem 4:__** BA' and AB' are chords of a circle that intersect at C. Find a relationship between the lengths of segments AC, BC, B'C and A'C.



**__Problem 5:__** ABC is a right triangle. AM is perpendicular from vertex A to the hypotenuse BC of the triangle. How many similar triangles are there?