IXL - Construct an equilateral triangle inscribed in a circle (Geometry practice)

The diagram below shows a nearly completed construction of an equilateral triangle inscribed in

⨀A

with a vertex at

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 an equilateral triangle inscribed in

⨀A

with a vertex at

Complete the construction.

Undo

Redo

Point

Segment

Ray

Line

Circle

Delete

key idea

An equilateral triangle has all three sides congruent and all angle measures equal to 60°.

Two chords in a circle are congruent if and only if their corresponding central angles are congruent.

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 the line through
A
and
B
.

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

Draw a circle with radius
A
C
centered at
C
.

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

Since

and

are all on

⨀

Since

and

are all on

⨀

This means that

So,

△

and

△

are congruent equilateral triangles.

Draw the segment between
B
and
D
.

Draw the segment between
D
and
E
.

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

To complete the construction of an equilateral triangle inscribed in

⨀A

with a vertex at

carry out the following step:

Draw the segment between
B
and
E
.

Since

△

and

△

are both equilateral,

∠

and

∠

are both 60°. So, the supplementary angles

∠

and

∠

are both 120°.

60°

120°

Also,

∠

= 60° + 60° = 120°. Since the central angles

∠

and

∠

are all congruent, so are the corresponding chords

, and

So,

△

is an equilateral triangle.

Looking for more? Try this:

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Teacher tools

Work it out

Not feeling ready yet? These can help:

W.9Arcs and chords

G.5Construct an equilateral triangle or regular hexagon

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