Lesson 7

Construction Techniques 5: Squares

Lesson Narrative

In this lesson, students apply their knowledge of constructing perpendicular lines and transferring distances to construct squares—first a square with a given side, and then a square inscribed in a circle. Students will need to recognize the structure of perpendicular parts (sides or diagonals) to identify an appropriate construction technique (MP7).

In the warm-up, students identify attributes belonging to categories of two-dimensional figures to review the definition of a square. The construction of the square inscribed in a circle provides the opportunity to preview the idea of symmetry that is developed later in the unit. Students also learn the term regular polygon to describe shapes that are both equilateral and equiangular, including squares.

If students have ready access to digital materials in class, they can choose to perform all construction activities with the GeoGebra Construction tool accessible in the Math Tools or available at https://www.geogebra.org/m/VQ57WNyR

Learning Goals

Teacher Facing

  • Construct a square.
  • Describe (orally and in writing) the diagonals of a square and use these conjectures to construct a square inscribed in a circle.

Student Facing

  • Let’s use straightedge and compass moves to construct squares.

Learning Targets

Student Facing

  • I can construct a square inscribed in a circle.
  • I can construct a square using a given segment for one of its sides.

CCSS Standards

Building On


Building Towards

Glossary Entries

  • angle bisector

    A line through the vertex of an angle that divides it into two equal angles.

  • circle

    A circle of radius \(r\) with center \(O\) is the set of all points that are a distance \(r\) units from \(O\)

    To draw a circle of radius 3 and center \(O\), use a compass to draw all the points at a distance 3 from \(O\).

  • conjecture

    A reasonable guess that you are trying to either prove or disprove.

  • inscribed

    We say a polygon is inscribed in a circle if it fits inside the circle and every vertex of the polygon is on the circle. We say a circle is inscribed in a polygon if it fits inside the polygon and every side of the polygon is tangent to the circle.


  • line segment

    A set of points on a line with two endpoints.

  • parallel

    Two lines that don't intersect are called parallel. We can also call segments parallel if they extend into parallel lines.

  • perpendicular bisector

    The perpendicular bisector of a segment is a line through the midpoint of the segment that is perpendicular to it. 

  • regular polygon

    A polygon where all of the sides are congruent and all the angles are congruent.

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