1. Similar Polygons /Dilations

2. Similar Polygons Corresponding angles are congruent.
Corresponding sides are proportional
Corresponding angles are congruent.
Which means what about the overall shape of the figure?
Same SHAPE, different SIZE

3. Example ABCD ~ TPOR Similarity Statement: Identifies similar
polygons and corresponding parts
Just like when congruent, order is
given in the statement
~ means similar
Key to Solving: Find the Scale Factor
Scale Factor: Corresponding sides in the figure that both have a measurement

4. What is the scale factor from
TPOR to ABCD?
Ratio
Denominator
Numerator

5. Solve for Missing Sides: Set up proportions, be consistent
(sides are proportional when similar)
Follow ABCD to TPOR
Solve for z
Solve for X
Scale Factor
Solve for y
Z is an angle.
Angles are CONGRUENT
5x = 24
x = 4.8
40 = 3z-20
60 = 3z
20 = z
25 = 3y
8.3 = y

6. ABC ~ EDC
ALWAYS RE-DRAW if corresponding parts are not matched up
Solve for x, y and z

7. Warm-up
Find x, y, and z

8. 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).

9. A (1,4) A ‘ (2,8) B (5,1) B ‘(10,2) C (0,0) C ‘ ( 0,0)
Given Triangle ABC, graph the image
Of ABC with a scale factor of 2.
(2x, 2y)
Pre-Image
Image
A (1,4)
A ‘ (2,8)
B (5,1)
B ‘(10,2)
C (0,0)
C ‘ ( 0,0)

11. Triangle ABC has vertices A ( 0,0) , B( 4,0) , C (0,5). Graph it
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?