2 Similar Triangles In order for two triangles to be similar: Their angles must be _____________Their ___________ sides must be ____________congruentcorrespondingproportional
3 Geometric MeanThe Altitude of a triangle is the _____________ segment from a _____________ to the ____________ side.The Altitude is called the Geometric Mean.Draw a picture:perpendicularvertexoppositeBDCA
4 Theorem 9.1altitudeIf the ______________ is drawn to the hypotenuse of a ___________ triangle, then the two triangles formed are ____________ to the ____________ triangle and to each other.Draw a picture and write the three SIMILARITY STATEMENTS:rightsimilaroriginalBADC
5 Example 1:A roof has a cross section that is a right triangle. The diagram shows the approximate dimensions of this cross section.a) Identify the similar triangles in the diagram.b) Find the height of h.
7 Theorem 9.2 In the diagram: In other words: In a right triangle, the altitude from the _____________ angle to the ____________ divides the hypotenuse into two segments. The length of the altitude is the ___________ _____________ of the lengths of the two segments.In the diagram:In other words:hypotenuserightmeangeometric
8 Theorem 9.3rightIn a right triangle, the altitude from the ___________ angle to the _____________ divides the hypotenuse into two segments. The length of each leg of the right triangle is the _________________ _________ of the lengths of the ____________ and the segment of the hypotenuse that is _____________ to the leg.In the diagram:In other words:hypotenusegeometricmeanhypotenuseadjacent