9.1 ( old geometry book ) similar triangles 5.4-9.1 hw quiz: wednesday special triangles test:...
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9.1 (old geometry book)
Similar Triangles
5.4-9.1 HW Quiz: Wednesday
Special Triangles Test: FRIDAY!
Similar Triangles
In order for two triangles to be
similar:1. Their angles must be _____________
2. Their ___________ sides must be ____________
congruent
corresponding
proportional
Geometric Mean
• The Altitude of a triangle is the _____________ segment from a _____________ to the ____________ side.
• The Altitude is called the Geometric Mean.
Draw a picture:
A
D
C
B
perpendicular
vertex opposite
Theorem 9.1
• If 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:
B
A
D
C
altitude
rightsimilar
original
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.
7.8 m 12.3 mh
14.6 m
D CA
B
Example 1 cont’d:
7.8 m 12.3 mh
14.6 m
D CA
B
Theorem 9.2 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:
AD BD
BD DC
D
B C
A
1
2
Part Altitude
Altitude Part
right hypotenuse
geometric mean
Theorem 9.3 In 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:
AC AB
AB AD D
B C
A
hyp leg
leg part
right
hypotenuse
geometric meanhypotenuse
adjacent
Example 2:
• Solve for the missing variable:
x
106
y
8
5
Homework
9.1 Worksheet