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In this diagram, line segment CD is the

perpendicular bisector of line segment
AB. Assume the conjecture that the set of
points equidistant from A and B is the
perpendicular bisector of AB is true. Is
point E closer to point A, closer to point B,
or the same distance between the points?
Explain how you know..

1 Answer

7 votes

Answer:

Point E is closer to point A

Explanation:

"I have added screenshot of the complete question as well as the

diagram"

- In this diagram, line segment CD is the perpendicular bisector of line

segment AB

∴ AB ⊥ CD

∵ CD intersect AB at M

∴ M is the mid-point of AB

∴ The length of AM = the length of MB

- Assume the conjecture that the set of points equidistant from A

and B is the perpendicular bisector of AB is true

∴ Any point lies on the line CD equidistant from A and B

- If point E lies on the line CD

∵ CD is the perpendicular bisector of AB

∵ E lies on CD

∴ The length of EA = The length of EB

- From the figure point E is on the left side of the line CD

∵ Point A is on the left side of the line CD

∵ Point B is on the right side of the line CD

∵ Point E is on the left side of the line CD

∴ The length of AE < The length of BE

Point E is closer to point A

In this diagram, line segment CD is the perpendicular bisector of line segment AB-example-1
User Navnath Godse
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