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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:. - PowerPoint PPT Presentation
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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 6.7Proportional Perimeters
Theorem
Theorem 6.7Proportional Perimeters
TheoremIf 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.
X Z
Y
9
C
B
A41 9
40
Theorem 6.8
Theorem 6.8Similar triangles have
corresponding altitudes proportional to the
corresponding sides.
Theorem 6.8Q
P RA
U
VW
T
TU
PQ
UV
QR
TV
PR
UW
QA
Theorem 6.9
Theorem 6.9
Similar triangles have corresponding angle
bisectors proportional to the corresponding sides.
Theorem 6.9
XV
U
T
BR
Q
P
TU
PQ
UV
QR
TV
PR
UX
QB
Theorem 6.10
Theorem 6.10
Similar triangles have corresponding medians
proportional to the corresponding sides.
Theorem 6.10
YV
U
T
MR
Q
P
TU
PQ
UV
QR
TV
PR
UY
QM
Theorem 6.11Angle Bisector
Theorem
Theorem 6.11Angle 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 6.11Angle Bisector
Theorem
D
C
BA
B
A
BC
AC
DB
AD
th vertex segment wi
th vertex segment wi
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.
K
x
LI
J
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.
E
DG F
. Find
. and
EC
DCGCFGCFAF
In the figure, ABC ~ GED.
A
80
30E
F GD
C
B
Assignment:
Pgs. 320-323 10-26 evens, 42-50 evens