IXL - Construct an angle bisector (Geometry practice)

The diagram below shows a nearly completed construction of the bisector of

∠

Complete the construction.

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Redo

Point

Segment

Ray

Line

Circle

Delete

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Learn with an example

question

The diagram below shows a nearly completed construction of the bisector of

∠

Complete the construction.

Undo

Redo

Point

Segment

Ray

Line

Circle

Delete

key idea

The diagonals

and

of a rhombus

have the following properties:

and

are the perpendicular bisectors of each other.

bisects angles

∠

and

∠

and

bisects angles

∠

and

∠

Constructing a rhombus can be helpful when constructing bisectors or perpendicular lines.

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
.

Mark the point where
⨀
A
and
A
C
intersect. Call it
D
.

Since

and

are both on

⨀

Draw a circle with radius
A
B
centered at
D
.

Draw a circle with radius
A
B
centered at
B
.

Mark the point other than
A
where
⨀
B
and
⨀
D
intersect. Call it
E
.

Since

and

are both on

⨀

Since

and

are both on

⨀

Since

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

To complete the construction of the bisector of

∠

carry out the following step:

Draw the line through
A
and
E
.

Since

quadrilateral

is a rhombus. So, the diagonal

is the bisector of

∠

Looking for more? Try these:

Lesson: Angle bisectors

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Teacher tools

Work it out

Not feeling ready yet? These can help:

C.6Angle bisectors

B.8Construct a congruent segment

O.8Properties of rhombuses

Lesson: Angle bisectors

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