IXL - Construct a perpendicular line (Geometry practice)

The diagram below shows a nearly completed construction of a line through

that is perpendicular to

Complete the construction.

Undo

Redo

Point

Segment

Ray

Line

Circle

Delete

ref_doc_title.

Learn with an example

question

The diagram below shows a nearly completed construction of a line through

that is perpendicular to

Complete the construction.

Undo

Redo

Point

Segment

Ray

Line

Circle

Delete

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.

Construct a segment

that has

as the midpoint.

Draw a circle with radius
A
B
centered at
A
.

Mark the point other than
B
where
⨀
A
and
line
A
B
intersect. Call it
C
.

Since

and

are both on

⨀

So,

is the midpoint of

Construct the perpendicular bisector of

Draw a circle with radius
B
C
centered at
B
.

Draw a circle with radius
B
C
centered at
C
.

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

Since

and

are both on

⨀

Since

and

are both on

⨀

So,

Similarly,

So,

and

are equidistant from

and

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

To complete the construction of a line through

that is perpendicular to

carry out the following step:

Draw the line through
D
and
E
.

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

This means that

⟂

and

passes through the midpoint of

which is

Since

is the same line as

is a line through

perpendicular to

Note that

could also have been drawn as

without marking the point

Looking for more? Try these:

Lesson: Perpendicular bisectors

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	06

SmartScore
out of 100
IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more

Teacher tools

Work it out

Not feeling ready yet? These can help:

B.9Perpendicular Bisector Theorem

B.8Construct a congruent segment

D.1Identify parallel, intersecting, and skew lines and planes

Lesson: Perpendicular bisectors

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!