Use Similar Right Triangles

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Presentation transcript:

Use Similar Right Triangles Ch 7.3

Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original right triangle.

Name 3 similar triangles? 1. Draw the smallest triangle. 2. Draw the middle triangle. 3. Draw the largest triangle. 4. Match up the angles. îSUT ~ îTUR ~ îSTR

Name the similar triangles, then find x. îEHG ~ îGHF ~ îEGF To find x make a ratio of the hypotenuses and the a ratio of 2 proportional legs.

Name the similar triangles and find x. îLKM ~ îMKJ ~ îLMJ

Find x and y. 72 21 y x

Find x.

Find x

Geometric Mean Altitude Theorem In a right triangle the altitude from the right angle to the hypotenuse divides the hypotenuse into 2 segments. The length of the altitude is the geometric mean of the lengths of the 2 segments

Finding the length of the altitude Set up a proportion to find BD. B C A D Find side AD. Plug values into

Find the amplitude, if these are right triangles Find the amplitude, if these are right triangles. One of these is not a right triangle 1. 2. 8.5 6.6 3. not right

Geometric Mean (Leg) Theorem In a right triangle, the altitude divides the hypotenuse into 2 segments. The length of each leg of each right triangle is the geometric mean of length of the hypotenuse and a segment of the hypotenuse

Find x and y y x 12.75 4.25

Find x

Find x and y y x +2 8 2

Find a

Find b

Find x and y 30 16 z x y |--------- 34 -------------|

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