D. N. A.

1) Find the scale factor of PQRS to ABCD.

2) Find the value of x.

3) Find the value of y.

4) Find the value of z.

P

Q

R

S30

15

x 21PQRS~ABCD A

B

C

D

12y

10 z

5) Find the perimeter of PQRS.

6) Find the perimeter of ABCD.

7) Find the ratio of the perimeter of PQRS to the perimeter of ABCD.

SAS Similarity Theorem• If one angle of one triangle is congruent to an

angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar.

K

J L

Y

X Z

ΔXYZ ~ ΔJKLthen

and XJ if

XZ

JL

XY

JK

Pantographass

Prove RTS ~ PSQS S (reflexive prop.) S

TR

QP

5

1512

4

16

4

20

5

SPQ SRT

SAS ~ Thm.

ST

SQ

SR

SP

)16(5)20(4 8080

Are the two triangles similar?

3

4

9

12

QT

NQ

N P

Q

R T

10

1512

9Not

Similar

2

3

10

15

RQ

PQ

NQP TQR

Determine the similar triangles.

5. Find x, AC, and ED.

E

D

BA

C

5x

151x

12

6. Find x, JL, and LM.

J

K

LN

M4

3x

18x16

7. Find x, EH, and EF.

5x

9

9

126EH

F

DG

In the figure, , and ABC and DCB are right angles. Determine which triangles in the figure are similar.

Are Triangles Similar?

A. ΔOBW ~ ΔITW

B. ΔOBW ~ ΔWIT

C. ΔBOW ~ ΔTIW

D. ΔBOW ~ ΔITW

In the figure, OW = 7, BW = 9, WT = 17.5, and WI = 22.5. Determine which triangles in the figure are similar.

Parts of Similar Triangles

ALGEBRA Given , RS = 4, RQ = x + 3, QT = 2x + 10, UT = 10, find RQ and QT.

Parts of Similar Triangles

Since

because they are alternate interior angles. By AA

Similarity, ΔRSQ ~ ΔTUQ. Using the definition of similar

polygons,

Substitution

Cross products

Parts of Similar Triangles

Answer: RQ = 8; QT = 20

Distributive Property

Subtract 8x and 30 from each side.

Divide each side by 2.

Now find RQ and QT.

Lesson 3 CYP3

A. 196 ft B. 39 ft

C. 441 ft D. 89 ft

INDIRECT MEASUREMENT On her trip along the East coast, Jennie stops to look at the tallest lighthouse in the U.S. located at Cape Hatteras, North Carolina. At that particular time of day, Jennie measures her shadow to be 1 feet 6 inches in length and the length of the shadow of the lighthouse to be 53 feet 6 inches. Jennie knows that her height is 5 feet 6 inches. What is the height of the Cape Hatteras lighthouse to the nearest foot?

Geometry – Practice WorkbookDo not write in the workbook.Write your answers on a separate sheet of paper.

Complete:p. 43 #1 – 8 allp. 42 #1 – 5 oddp. 41 # 1 – 15 odd