Download Ohio Content Standards

Lesson 6-5
Parts of
Similar Triangles
Ohio Content Standards:
Ohio Content Standards:
Estimate, compute and solve
problems involving real numbers,
including ratio, proportion and
percent, and explain solutions.
Ohio Content Standards:
Use proportional reasoning and apply
indirect measurement techniques,
including right triangle trigonometry
and properties of similar triangles, to
solve problems involving
measurements and rates.
Ohio Content Standards:
Use scale drawings and right
triangle trigonometry to solve
problems that include unknown
distances and angle measures.
Ohio Content Standards:
Apply proportional reasoning to
solve problems involving indirect
measurements or rates.
Ohio Content Standards:
Describe and apply the properties
of similar and congruent figures;
and justify conjectures involving
similarity and congruence.
Ohio Content Standards:
Make and test conjectures about
characteristics and properties
(e.g., sides, angles, symmetry) of
two-dimensional figures and
three-dimensional objects.
Ohio Content Standards:
Use proportions in several forms
to solve problems involving similar
figures (part-to-part, part-to-whole,
corresponding sides between
figures).
Ohio Content Standards:
Use right triangle trigonometric
relationships to determine lengths
and angle measures.
Ohio Content Standards:
Apply proportions and right
triangle trigonometric ratios to
solve problems involving missing
lengths and angle measures in
similar figures.
Theorem 6.7
Proportional Perimeters
Theorem
Theorem 6.7
Proportional Perimeters
Theorem
If two triangles are similar,
then the perimeters are
proportional to the measures
of corresponding sides.
ABC ~ XYZ
XZ = 40, YZ = 41,
XY = 9, and AC = 9, find
the perimeter of ABC.
B
Y
A
41
9
X
40
Z
9
C
Theorem 6.8
Theorem 6.8
Similar triangles have
corresponding altitudes
proportional to the
corresponding sides.
Theorem 6.8
U
Q
T
P
A
R
QA PR QR PQ



UW TV UV TU
W
V
Theorem 6.9
Theorem 6.9
Similar triangles have
corresponding angle
bisectors proportional to
the corresponding sides.
Theorem 6.9
Q
U
T
P
B
R
QB PR QR PQ



UX TV UV TU
X
V
Theorem 6.10
Theorem 6.10
Similar triangles have
corresponding medians
proportional to the
corresponding sides.
Theorem 6.10
Q
U
T
P
M
R
QM PR QR PQ



UY TV UV TU
Y
V
Theorem 6.11
Angle Bisector
Theorem
Theorem 6.11
Angle Bisector
Theorem
An angle bisector in a triangle
separates the opposite side
into segments that have the
same ratio as the other two
sides.
Theorem 6.11
Angle Bisector
Theorem
C
AD AC
segment wi th vertex A


DB BC
segment wi th vertex B
A
D
B
ABC ~ MNO and
BC = 1/3 NO.
Find the ratio of the
length of an altitude of
ABC to the length
of an altitude of MNO.
In the figure, EFG ~ JKL.
ED is an altitude of EFG,
and JI is an altitude of JKL.
Find x if EF = 36, ED = 18,
and JK = 56.
J
x
I
E
D
G
F
L
K
In the figure,
ABC ~
GED.
AF  CF and FG  GC  DC .
Find EC.
B
E
30
A
F
80
G
C
D
Assignment:
Pgs. 320-323
10-26 evens,
42-50 evens