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