Lesson 7: Construction Techniques 5: Squares
About this lesson
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 warmup, students identify attributes belonging to categories of twodimensional 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 Warmup: 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 Cooldown: 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
Glossary:

regular polygon  A polygon where all of the sides are congruent and all the angles are congruent.
 Access the complete Geometry Course glossary.
Standards:
 This lesson builds on the standards: CCSS.5.G.B.3MS.5.G.3CCSS.HSGCO.A.1MS.GCO.1CCSS.HSGCO.D.12MS.GCO.12MO.5.GM.A.1MO.G.CO.A.1MO.G.CO.D.11
 This lesson builds towards the standards: CCSS.HSGCO.A.3MS.GCO.3CCSS.HSGCO.D.13MS.GCO.13MO.G.CO.A.3MO.G.CO.D.11
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