IXL - Construct the midpoint or perpendicular bisector of a segment (Geometry practice)

Mark the midpoint of

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Point

Segment

Ray

Line

Circle

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question

Mark the midpoint of

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Point

Segment

Ray

Line

Circle

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key idea

The Perpendicular Bisector Theorem states that a point is on the perpendicular bisector of a segment if and only if it is equidistant from the endpoints of the segment.

is on the perpendicular bisector of

if and only if

≅

solution

Part of the construction was done for you. Here are the steps to create this part of the construction.

Start with the objects in the diagram below.

Draw a circle with radius
A
B
centered at
A
.

Draw a circle with radius
A
B
centered at
B
.

Mark the points where
⨀
A
and
⨀
B
intersect. Call them
C
and
D
.

Since

and

are both on

⨀

Since

and

are both on

⨀

So,

Similarly,

So,

and

are equidistant from

and

Draw the line through
C
and
D
.

Recall that the set of points equidistant from

and

form the perpendicular bisector of

Since

and

are equidistant from

and

they lie on the perpendicular bisector. So,

is the perpendicular bisector of

start of large bold text, Complete the construction., end of large bold text

To complete the construction of the midpoint of

carry out the following step:

Mark the point where
line
C
D
and
segment
A
B
intersect. Call it
E
.

Since

is the perpendicular bisector of

the intersection

is the midpoint of

Looking for more? Try these:

Lesson: Perpendicular bisectors

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Not feeling ready yet? These can help:

B.9Perpendicular Bisector Theorem

Lesson: Perpendicular bisectors

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