In the figure below, if BE is the perpendicular bisector of AD , what is the value of x?

A. 2
B. 3
C. 4
D. 5

Question

In the figure below, if BE is the perpendicular bisector of AD , what is the value of x? 

A.	2
	B.	3
	C.	4
	D.	5

anonymous · Answer

attachment

ash2326 · Answer

Triangles ABE and DBE, 
can you prove them congruent?

anonymous · Answer

@ash2326 um yes? im not quite sure how to?

ash2326 · Answer

OK< I'll guide you

anonymous · Answer

@ash2326 thank you!

ash2326 · Answer

|dw:1366312920656:dw|

ash2326 · Answer

We know BE is perpendicular bisector so 
$$AE= ED$$|dw:1366313039641:dw|

anonymous · Answer

Oh I see, so the same side and same angle measure makes them congruent. @ash2326

ash2326 · Answer

We need to have one angle and two sides equal. Can you tell what all parameters are congruent?

anonymous · Answer

is it AB and DB? @ash2326

ash2326 · Answer

We don't know that now, first we'll prove the two triangles congruent.
Angle BEA= Angle BED ( since BE is perpendicular bisector)

ash2326 · Answer

side BE = BE ( common side)
SO using SAS ( Side Angle Side)
ABE = DBE
Do you understand this @kaylamalik_xo

anonymous · Answer

oh ok, so the ab is not congruent with db yet... its EB that makes them congruent?

anonymous · Answer

@ash2326

ash2326 · Answer

Exactly, now the triangles are proven congruent
We can have AB=DB

anonymous · Answer

so the equation would be 3x+4=x+12? @ash2326

ash2326 · Answer

Correct, you can find x from this, can't you?