Which statement is not necessarily true?
given: line de is the perpendicular bisector of line jl
for my answer, i put that dk = ke
can someone check my answer : ) youu!

The given relationship between lines and is found by noting the

given relationship between the lines.

The statement that is not necessarily true is; DK = KE

Reasons:

⊥ Given in the question

is the perpendicular bisector of

Therefore, = Definition of bisected line

Point K is the midpoint definition of point of bisection of line

=

∠JKD = ∠LKD = 90°, definition of perpendicular line

In ΔDKJ, and ΔDLK, = , = ,and ∠JKD = ∠LKD

Therefore;

ΔDKJ ≅ ΔDLK by Side-Angle-Side, SAS rule of congruency

Therefore;

DJ = DL by Congruent Parts of Congruent Triangles are Congruent,

CPCTC  also by the equidistant of points on a perpendicular bisector from

the end points of the bisected line.

Which gives;

The only statement that is not necessarily true is the statement;

DK = KE , given that the relationship between DK and KE is not specified.

Learn more about perpendicular bisection here:

link

A isn't always true since we can slide D and E up so that DK = KE is false

B is always true by what is set up. We're given that DE is the perpendicular bisector, so DE is perpendicular to JL

C is always true because of the "bisector" portion (aka cuts it in half)

D is always true, which can be proven through the use of SAS and then CPCTC

So you have the right answer, which is choice A

The second one is the answer