Lesson (6.5) Parts of Similar Triangles BC A D Altitude BC A N Median Angle bisector BC A M

Lesson (6.5) Parts of Similar Triangles

B C

A

D

Altitude

B C

A

N

Median Angle bisector

B C

A

M

E F

D

X

Y

Z

B C

A

M

L

N ~

DE

AB EF

BC FD

CA DX

AM EY

BN FZ

CL DEFofperimeter

ABCofperimeter

If then

The perimeter of the triangle is the sum of the measures of its sides

Angle bisector Theorem

B C

A

D

If AD is an

angles bisector then

DC

BD AC

BA

Check for understandingCheck for understanding

Find the perimeter of the given triangle

37,6,5,~, DEandACBCABDEFABCifDEF

• Step1: Set up proportions.

• Step3: Cross multiply and solve for x.

x

18

3

5 545 x

5 58.10x

DE

AB EF

BC FD

CA DEFofperimeter

ABCofperimeter

• Step2: substitute the values.

3

5 EF

6 FD

7 x

18

Check for understandingCheck for understanding

Find x

• Step1: Set up proportions.

• Step2: Cross multiply and solve for x.

13

5.6

12

x 7813 x 13 13

6x

12

x 13

5.6

Check for understandingCheck for understanding

Find x

• Step1: Set up proportions.

• Step2: Cross multiply and solve for x.

3

420

x604 x

4 415x

x

20 12

16

Check for understandingCheck for understanding

Find x

• Step1: Use the angle bisector Theorem.

• Step2: Cross multiply and solve for x.

8

3

18

x 548 x 8 8

75.6x

18

x 24

9

HomeworkHomeworkHomeworkHomework

Page 320 – 322

#s (10, 14, 18, 22, 24)

Written Exercises page 320Written Exercises page 320

Find the perimeter of the given triangle

84,5,12,~, DEandFEFDCDFDEBCDifBCD

• Step1: Set up proportions.

• Step3: Cross multiply and solve for x.

• Step2: substitute the values.

10)

Written Exercises page 320Written Exercises page 320

Find the perimeter of the given triangle

5,3,4,~, CBandDBCDCBDABCifABC

• Step1: Set up proportions.

• Step3: Cross multiply and solve for x.

• Step2: substitute the values.

14)

Written Exercises page 320Written Exercises page 320

5.7

,15,17,

,~

EHand

ADACEGFofalttitudeanisEH

ACBofalttitudeanisADEGFACBifEGfind

• Step1: Set up proportions.

• Step3: Cross multiply and solve for x.

• Step2: substitute the values.

18)

Find x

• Step1: Set up proportions.

• Step2: Cross multiply and solve for x.

Written Exercises page 321Written Exercises page 321

22)

Find x

• Step1: Use the angle bisector Theorem.

• Step2: Cross multiply and solve for x.

Written Exercises page 321Written Exercises page 321

24)