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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 please check my answer :) Thank youu!

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 please check my answer class=

Respuesta :

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 given relationship between lines [tex]\mathbf{\overline {DE}}[/tex] and [tex]\mathbf{\overline {JL}}[/tex] is found by noting the

given relationship between the lines.

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

Reasons:

[tex]\overline {DE}[/tex] ⊥ [tex]\overline {JL}[/tex] Given in the question

[tex]\overline {DE}[/tex] is the perpendicular bisector of [tex]\overline {JL}[/tex]

Therefore, [tex]\overline {JK}[/tex] = [tex]\mathbf{\overline {KL}}[/tex] Definition of bisected line [tex]\overline {JL}[/tex]

Point K is the midpoint [tex]\overline {JL}[/tex] definition of point of bisection of line [tex]\overline {JL}[/tex]

[tex]\overline {JK}[/tex] = [tex]\overline {KL}[/tex]

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

In ΔDKJ, and ΔDLK, [tex]\overline {JK}[/tex] = [tex]\overline {KL}[/tex], [tex]\overline {DK}[/tex] = [tex]\overline {DK}[/tex],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:

https://brainly.com/question/1761937

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