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Presentation transcript:

DO NOW

Geometric Means in Right Triangles

C A D B C C D B A D

C A B C C D B A D

The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse. 𝑨𝑫 𝑪𝑫 = 𝑪𝑫 𝑫𝑩

ALTITUDE RULE The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse.

X = 𝟏 𝟐 𝑥 2 = 2 8 X =𝟐𝟕 3 9 = 9 𝑥 40 𝑥 = 𝑥 10 X =𝟐𝟎

AB CB The leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse. = CB DB Leg Rule

AB CA The leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse. = CA AD Leg Rule

X = 6 9 𝑥 = 𝑥 4 X = 2 𝟕𝟎 20 𝑥 = 𝑥 14 X = 100 𝑥 60 = 60 36

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