7th Grade Math

294 Proportions and Similarity

Similar Figures

Words Two figures are similar if

• the corresponding sides are proportional, and


• the corresponding angles are congruent.

Models #

"$

&

%'

Symbols ABC ∼ DEF

corresponding sides: _ABDE = _BCEF = _DFAC

corresponding angles: ∠A  ∠D; ∠B  ∠E; ∠C  ∠F

Identify Similar Figures

Which trapezoid below is similar to &

'

%

( 12

trapezoid DEFG?^4

43

1 2

14

6

9

; :

8

9

3

.

+

• 
  

,

10

5

Find the ratios of the corresponding sides to see if they are

the same.

Trapezoid PQRS Trapezoid WXYZ Trapezoid JKLM

_EF

QR^ =

_^4

6 or^

_^2

3

_EF

XY^ =

_^4

3

_EF

KL^ =

_^4

5

_FG

RS^ =

_^12

14 or^

_^6

7

_FG

YZ^ =

_^12

9 or^

_^4

3

_FG

LM^ =

_^12

10 or^

_^6

5

Not similar Similar Not similar

So, trapezoid WXYZ is similar to trapezoid DEFG.

a. Which triangle below is similar to %

' &

15

triangle DEF? 6

9

:; 20

8

"

$ #

4

12

4

3

(^56)
3
Geometry Symbols
∼ is similar to; has the
same shape
 is congruent to; has the
same size and shape
A rule for determining that
two triangles are similar is
Side-Side-Side. It states
that two triangles are
similar if corresponding
side lengths are
proportional. The Angle-
Angle rule states that two
triangles are similar if
corresponding angles have
equal measures.
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293_303_C05_L3_895130.indd 294 12/29/09 1:09 PM