In ∆ABC if XY BC, In ∆ABC if XY AB

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Triangle  Proportionality  and  Its  Converse    

 

     

   

Name    _________________________________   Date  ___________________      Period  _______  

If a line is parallel to one side of a triangle and intersects the other two sides, then the line divides those sides proportionally. A

In ∆ABC if XY ║ BC,

X

Y

B

C

 

       

If a line is parallel to one side of a triangle and intersects the other two sides, then the line divides those sides proportionally. A X

B

       

Y

In ∆ABC if XY ║ AB,

C

 

   

If a line is parallel to one side of a triangle and intersects the other two sides, then the line divides those sides proportionally. A

In ∆ABC if XY ║ AC,

X

B

C

Y

 

         

Statements

Reasons

Given: ∆ABC and XY ║ BC Prove:

BX XA

=

YC YA

A

2

X 1

B

         

3

Y 4

C

 

© iTutoring.com Triangle  Proportionality  and  Its  Converse  (Side  Splitter  Theorem)   Pg.  2  

   

Use the Side Splitter Theorem to solve for x.

6

9

x

2

 

         

Use the Side Splitter Theorem to solve for x.

12 x

10

           

50

 

© iTutoring.com Triangle  Proportionality  and  Its  Converse  (Side  Splitter  Theorem)   Pg.  3  

     

Use the Side Splitter Theorem to solve for x.

x+4

2x

12

9

 

         

Converse: If a line inside a triangle intersects two sides and divides those sides into corresponding sides of proportional lengths, then the line is parallel to the third side.

XA

A

BX

X

B

       

If

BX CY = XA YA

YA

Y CY

C  

© iTutoring.com Triangle  Proportionality  and  Its  Converse  (Side  Splitter  Theorem)   Pg.  4  

   

Determine if XY ║ BC

A 10

20

Y

8

4

X

B

C  

           

Determine if XY ║ AB

A

3

Y 10

12

4

B

X

C  

© iTutoring.com Triangle  Proportionality  and  Its  Converse  (Side  Splitter  Theorem)   Pg.  5