january 3, 2017 do now today i can map similar figures hw: p...

similarity transformation jan 34.notebook January 05, 2017

January 3, 2017

• Do Now

• Today I can map similar figures onto one another

HW: p 110 14, 1720

CR 6 due Friday Reminders:

Quiz Tues Jan 10

Benchmark Exam Jan 19 & 20

Chapter test Feb 2

Do NowGraph Rectangle A(1,1), B(4,1), C(4,2), D(1,2)

After a dilation, A'B' = 6, state the scale factor.

Graph the dilation (center origin) of ABCD.


Figures with the same shape, but not necessarity the same size are said to be similar.

Two figures are similar if and only if one figure can be mapped onto the other figure by a series of rigid motions and/or dilations.

Name the transformations


Answer count carefully!

Sketch rAC(DB,2( ABC))

A

B C

let's try it on your dry erase board

http://www.mathopolis.com/questions/q.php?id=781&site=1&ref=/geometry/similar.html&qs=781_3272_6050_6051_6052_3273_3274_3275_631_632_1802_1803


Sketch the similarity transformation

DA,2 ( DC,3 (ABC)) tip: make your sketch of ABC small

What is the scale factor of this transformation?

A

B

C

Like your HWThe point (4,10) is a vertex of a triangle. The triangle is reflected about the yaxis, dilated by a scale factor of 2 with origin as the center of dilation, then translated up 5.

What are the final coordinate of this vertex?

Solution: Start with (4,10)

reflect on y axis (4,10)

dilate by 2 (8, 20)

translate up 5 (8, 25)


A tranformation changes the size of a figure but maintains its shape.

What do you know about the transformation?

Write your answer on a post it note.

January 4, 2017

• Do Now

• HW ?s

• Today I can find corresponding sides of similar figures

HW: p 105 18 Reminders:

Quiz Tues Jan 10


Chapter Test Feb 2


3

Do NowThe perimeters of 2 similar pentagons ABCDE and FGHJK are in the ratio of 3 to 2. Two corresponding sides are labeled 4.5 and x. Find HJ

(19,12)

(37,12)


Facts about similar triangles

Are these two triangles similar?

If triangles are similar, what do you know about their corresponding sides?


Recall what we learned before break

Put this into words...

ratio of

sides

ratio

of perimeter

ratio

of area

P =

A =P=

A=


Example

△ABC ~ △XYZ. The ratio of their perimeters is 1:3.

What is the ratio of the sides?

Find the length of

Find the ratio of the areas?

34

5A

B C

X

YZ

XZ

Given: ∆PQR ~ ∆TSR, QR = 5, RS = 10

What similarity transformaon can map ∆PQR to ∆TSR?

List all congruent angles and proporonal sides.

P

QR S

T

• Today I can recognize similar triangles & their corresponding parts.


C

A

T

D

O

G

CAT and DOG are equilateral triangles. CAT ~ DOG. CA = 1, DG = 3

What similarity transformaon can map CAT to DOG?

List all congruent angles and proporonal sides.


Given: Circle A has radius 4 and Circle B has radius 12

What similarity transformaon can map Circle A to Circle B?

A B


All circles are similar!


Write your answer on a post it note.

△ABC ~ △XYZ and have a scale factor (or similarity ratio) of 3:2

What is the ratio of their perimeter?

What is the ratio of their areas?

January 5, 2017

• Do Now

• HW ?s

• Today I can prove 2 triangles are similar using AA

HW: p 289 1, 3, 8, 10, 11

Reminders:

Quiz Tues Jan 10


Practice Test Jan 23

Chapter Test Feb 2


Do NOw!!!! Y

Z

X

U

VZ

Y

Z

X

Which triangle is not similar to the other three and why???


FG

FG =12

6

9

AngleAngle Similarity Theorem

Two triangles are similar if 2 angles of one triangle are congruent to two angles of the other triangle.


State if the triangles in each pair are similar.

If similar, write the similarity statement.

1) ∆____ ~ ∆_____

2) ∆____ ~ ∆_____


If similar, write the similarity statement.


Solve for x and y.

3) ∆ABC ~ ∆EFG

x = ___ , y = ____

(x+15)°A

B

Cy°

E

F

G2x°50°

Solve for x and y. 4) ∆CAT ~ ∆DOG

x = ___ , y = ____

D

O

G(x + 75)O

(3x)O

C

A

Ty°

or try the challenge15


Reminders:

> Quiz Wed 1.11

> Benchmark 1.19 & 1.20

> Practice Test Mon 1.23

> Test Wednesday 2.2

Homework: p289 #1, 3, 8, 10, 11


115O

25O 25O

40O

45O45O


Solve for x and y.

3. ∆ABC ~ ∆EFG

x = ___ , y = ____

4. ∆CAT ~ ∆DOG

x = ___ , y = ____

(x+15)°A

B

C

E

F

G2x°

y°

50°

D

O

G

C

A

T

(x + 75)O

(3x)O y°

• Today I can prove two triangles similar.

january 3, 2017 do now today i can map similar figures hw: p...

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