3.4b: Similar Polygons/Dilations p. 346-353. Similar Polygons Corresponding sides are proportional...

3.4b: Similar Polygons/Dilationsp. 346-353

Similar Polygons

• Corresponding sides are proportional•Corresponding angles are congruent.

Which means what about the overall shape of the figure?

Same SHAPE, different SIZE

ExampleABCD ~ 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 FactorScale Factor: Corresponding sides in the figure that both have a measurement

PO

BC

scale

:

TPOR toABCDfor factor

NumeratorDenominator

Ratio

3

5 reduced

6

10 TPOR toABCD fromfactor scale theis 3

5

What is the scale factor from TPOR to ABCD?

5

3

10

6

BC

PO

ABCD

TPOR

Solve for Missing Sides: Set up proportions, be consistent (sides are proportional when similar)

Follow ABCD to TPORSolve for X

x

8

3

5

Scale Factor

5x = 24 x = 4.8

Solve for y

53

5 y

25 = 3y

8.3 = y

Solve for z

Z is an angle.

Angles are CONGRUENT

40 = 3z-20

60 = 3z

20 = z

ABC ~ EDC

Solve for x, y and z ALWAYS RE-DRAW if corresponding parts are not matched up

Find x, y, and z

Warm-up

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 Image

A (1,4)

(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?

homework