Transcript Similar Polygons - Matthew A. Guerra

Similar Polygons /Dilations
Similar Polygons
• Corresponding sides are proportional
•Corresponding angles are congruent.
Which means what about the overall shape of the figure?
Same SHAPE, different SIZE
Example
ABCD ~ TPOR
~ means similar
Similarity Statement: Identifies similar
polygons and corresponding parts
Just like when congruent, order is
given in the statement
Key to Solving: Find the Scale Factor
Scale Factor: Corresponding sides in the figure that both have a measurement
scale factor for ABCD to TPOR
BC 10
5
:

reduced
PO 6
3
5
is the scale factor from ABCD to TPOR
3
What is the scale factor from
TPOR to ABCD?
Ratio
Numerator
Denominator
TPOR PO 6 3

 
ABCD BC 10 5
Solve for Missing Sides: Set up proportions, be consistent
(sides are proportional when similar)
Follow ABCD to TPOR
Scale Factor Solve for X
5 8

3 x
5x = 24
x = 4.8
Solve
for y
5 y

3 5
Solve for
z
Z is an angle.
Angles are CONGRUENT
40 = 3z-20
25 = 3y
60 = 3z
8.3 = y
20 = z
ABC ~ EDC
Solve for x, y and z
ALWAYS RE-DRAW if
corresponding parts are not
matched up
Warm-up
Find x, y, and z
A dilation is a transformation that changes the size of a
figure but not its shape. The pre-image and the image are
always similar shapes.
A scale factor for a dilation with a center at the origin is k, which is found by
multiplying each coordinate by k: (a, b)  (ka, kb).
Given Triangle ABC, graph the image
Of ABC with a scale factor of 2.
Pre-Image
A (1,4)
Image
(2x, 2y)
A ‘ (2,8)
B (5,1)
B ‘(10,2)
C (0,0)
C ‘ ( 0,0)
Triangle ABC has vertices A ( 0,0) , B( 4,0) , C (0,5). Graph it
1) If the coordinates of each vertex of ABC are increased by 2,
will the new triangle be similar to triangle ABC (Graph it)? Why or why not?
2) If the coordinates of each vertex of Triangle ABC are multiplied by 2,
will the new triangle be similar to Triangle ABC (Graph it)? Why or why not?