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.
similarity transformation jan 34.notebook January 05, 2017
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
similarity transformation jan 34.notebook January 05, 2017
Answer count carefully!
Sketch rAC(DB,2( ABC))
A
B C
let's try it on your dry erase board
similarity transformation jan 34.notebook January 05, 2017
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)
similarity transformation jan 34.notebook January 05, 2017
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
Benchmark Exam Jan 19 & 20
Chapter Test Feb 2
similarity transformation jan 34.notebook January 05, 2017
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)
similarity transformation jan 34.notebook January 05, 2017
Facts about similar triangles
Are these two triangles similar?
If triangles are similar, what do you know about their corresponding sides?
similarity transformation jan 34.notebook January 05, 2017
Recall what we learned before break
Put this into words...
ratio of
sides
ratio
of perimeter
ratio
of area
P =
A =P=
A=
similarity transformation jan 34.notebook January 05, 2017
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.
similarity transformation jan 34.notebook January 05, 2017
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.
• Today I can recognize similar triangles & their corresponding parts.
Given: Circle A has radius 4 and Circle B has radius 12
What similarity transformaon can map Circle A to Circle B?
A B
• Today I can recognize similar triangles & their corresponding parts.
All circles are similar!
similarity transformation jan 34.notebook January 05, 2017
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
Benchmark Exam Jan 19 & 20
Practice Test Jan 23
Chapter Test Feb 2
similarity transformation jan 34.notebook January 05, 2017
Do NOw!!!! Y
Z
X
U
VZ
Y
Z
X
Which triangle is not similar to the other three and why???
similarity transformation jan 34.notebook January 05, 2017
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.
similarity transformation jan 34.notebook January 05, 2017
State if the triangles in each pair are similar.
If similar, write the similarity statement.
1) ∆____ ~ ∆_____
2) ∆____ ~ ∆_____
State if the triangles in each pair are similar.
If similar, write the similarity statement.
similarity transformation jan 34.notebook January 05, 2017
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
similarity transformation jan 34.notebook January 05, 2017
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
State if the triangles in each pair are similar.
115O
25O 25O
40O
45O45O
similarity transformation jan 34.notebook January 05, 2017
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.
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