8.4 - Using Similar Right Triangles, Exams of Geometry

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Right Triangle Similarity Theorem

B

A

C

In a right triangle, analtitude drawn from thevertex of the right angleto the hypotenuse formstwo right similar triangles.

D

Sketch the triangles and then write a similarity statement comparing thetriangles.

POK

Practice 2 Write a similarity statement comparing the triangles. You may want tosketch the three right triangles to help you out.

Using Similar Triangles to Find Missing Parts Find the missing variable.1)

Using Similar Triangles to Find Missing Parts Find the missing variable.3)

Using Similar Triangles to Find Missing Parts Find the missing variable.4)

Geometric Mean The geometric mean of two positivenumbers is the positive square root of theirproduct. So the geometric mean of

a

and

b

is the positive number

x

such that:

Finding the Geometric Mean You’ve actually may have done somethinglike this in the previous problems whenyou set up certain proportions such as:

Geometric Mean^ Find the geometric mean of each pair of numbers. Ifnecessary, give the answer in simplest radical form.8)

14 and 20

25 and 35

Solving Missing Parts using the Geometric MeanGeometric Mean (Altitude) Theorem

POK

In a right triangle, the altitude from the right angle tothe hypotenuse divides the hypotenuse into two segments.The length of the altitude is the geometric mean of thelengths of the two segments of the hypotenuse. Note:

Use can use this when the big hypotenuse is dividedinto smaller parts.

Using the Geometric Mean to Find Missing Parts Find the missing variable.4 again)

Using the Geometric Mean to Find Missing PartsFind the missing variable.5 again)

Using the Geometric Mean to Find Missing PartsFind the missing variable.12)