Geometry Chapter 7 Similarity Review

1
Chapter 7 - Similarity
2
Chapter 7 - Similarity
3
Chapter 7 - Similarity
4
Theorem 7 4 Side Splitter Thm

• If a line is // to one side of a ? and intersects
  the other two sides, then it divides those sides
  proportionally.

A
short white piece
short orange piece

Long orange piece
Long white piece
E
or
AE
CE

BF
FC
B
C
F
5
Thm 7 5 ? - ?- Bisector Thm

• If a ray bisects an ? of a ?, then it divides the
  opposite side into 2 segments that are
  proportional to the other 2 sides of the ?.

Paraphrase Side compares to
other side the way piece compares to piece
PS
PQ
or

SR
QR
R
Q
Side compares to its piece the way other
side compares to its piece
PS
SR

(
QR
PQ
P
S
6
7-3
?
?
7
Altitude Corollary

• The length of the altitude to the hypotenuse of a
  right ? is the geometric mean of the lengths of
  the segment of the hypotenuse.
• The altitude splits the hyp. Into 2 segments.

?
x
h

y
h
8
Leg Corollary
Adj Part of Hyp
Leg

Whole hypotenuse
Leg
9
Altitude Corollary
Part of Hypotenuse
Altitude

Other part hyp
Altitude
10
What is a geometric mean?

• When the same number appears twice in a
  proportion

a
x
Extreme

Geometric Mean
x
d
Geometric Mean
Extreme