Lesson plan

Lesson 7: Construction Techniques 5: Squares

teaches Alabama State Standards Geo-30.
teaches Alabama State Standards Geo-29.b.
teaches Alabama State Standards Geo-29.a.
teaches Alabama State Standards Geo-29.
teaches Arizona State Standards G.G-CO.D.13
teaches Arizona State Standards G.G-CO.D.12
teaches Arizona State Standards G.G-CO.A.1
teaches Common Core State Standards MP5 http://corestandards.org/Math/Practice/MP5
teaches Common Core State Standards MP6 http://corestandards.org/Math/Practice/MP6
teaches Common Core State Standards HSG-CO.D.13 http://corestandards.org/Math/Content/HSG/CO/D/13
teaches Common Core State Standards MP7 http://corestandards.org/Math/Practice/MP7
teaches Colorado State Standards HS.G-CO.D.13.
teaches Colorado State Standards HS.G-CO.D.12.
teaches Colorado State Standards HS.G-CO.A.1.
teaches Georgia State Standards MGSE9-12.G.CO.13.
teaches Georgia State Standards MGSE9-12.G.CO.12.
teaches Georgia State Standards MGSE9-12.G.CO.1.
teaches Kansas State Standards G.CO.11.
teaches Minnesota State Standards
teaches Minnesota State Standards
teaches Ohio State Standards G.CO.13.
teaches Ohio State Standards G.CO.1.
teaches Pennsylvania State Standards CC.2.3.HS.A.4.
teaches Pennsylvania State Standards CC.2.3.HS.A.1.

Lesson 7: Construction Techniques 5: Squares

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. 

Lesson overview

  • 7.1 Warm-up: Which One Doesn’t Belong: Polygons (5 minutes)
  • 7.2 Activity: It’s Cool to Be Square (15 minutes)
    • Digital applet in this activity
  • 7.3 Activity: Trying to Circle a Square (15 minutes)
    • Digital applet in this activity
    • Includes "Are you Ready for More?" extension problem
  • Lesson Synthesis
  • 7.4 Cool-down: Build a House (5 minutes) 

Learning goals:

  • 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.

Learning goals (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.

Required materials:

  • Geometry toolkits


  • regular polygon - A polygon where all of the sides are congruent and all the angles are congruent.
  • Access the complete Geometry Course glossary. 


  • This lesson builds on the standards: CCSS.5.G.B.3MS.5.G.3CCSS.HSG-CO.A.1MS.G-CO.1CCSS.HSG-CO.D.12MS.G-CO.12MO.5.GM.A.1MO.G.CO.A.1MO.G.CO.D.11
  • This lesson builds towards the standards: CCSS.HSG-CO.A.3MS.G-CO.3CCSS.HSG-CO.D.13MS.G-CO.13MO.G.CO.A.3MO.G.CO.D.11






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