IXL - Construct a square (Geometry practice)

The diagram below shows a partly completed construction of a square with side

Complete the construction.

Undo

Redo

Point

Segment

Ray

Line

Circle

Delete

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Learn with an example

question

The diagram below shows a partly completed construction of a square with side

Complete the construction.

Undo

Redo

Point

Segment

Ray

Line

Circle

Delete

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 the line through
A
and
B
.

Draw a circle with radius
A
B
centered at
B
.

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 a line through

perpendicular to

Draw a circle with radius
A
C
centered at
A
.

Draw a circle with radius
A
C
centered at
C
.

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

Since

and

are both on

⨀

Since

and

are both on

⨀

So,

Draw the line through
B
and
D
.

△

is an isosceles triangle with congruent sides

and

so the line from the vertex

to the midpoint of

which is

is perpendicular to

So,

⟂

Draw the second side of the square.

Mark a point where
line
B
D
and
⨀
B
intersect. Call it
E
.

Draw the segment between
B
and
E
.

Since

and

are both on

⨀

Draw the remaining two sides of the square.

Draw a circle with radius
A
B
centered at
A
.

Draw a circle with radius
B
E
centered at
E
.

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

To complete the construction of a square with side

carry out the following steps:

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

Draw the segment between
E
and
F
.

Draw the segment between
A
and
F
.

Since

and

are both on

⨀

Since

and

are both on

⨀

∠

is a right angle since

is perpendicular to

is a rhombus because its four sides are congruent to each other. Since

is a rhombus with a right angle, it is a square.

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Teacher tools

Work it out

Not feeling ready yet? These can help:

B.15Construct the midpoint or perpendicular bisector of a segment

B.8Construct a congruent segment

O.8Properties of rhombuses

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