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GPS Alignment: Instructor Page
Week 12: Geometry - Quadrilaterals


Two Squares (Printable PDF)

Pick a point P on the line segment AB and make squares: A side of one square is AP and a side of the other square is PB. Where should the point P be located to satisfy the condition that the sum of the areas of the two squares is a minimum? Explain.

 

GPS

As seen in Problem Exploration

M7G1.  Students will construct plane figures that meet given conditions.

a. Perform basic constructions using both compass and straight edge, and appropriate technology. Constructions should include copying a segment; copying and angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
 

Students can either use GSP or construct the squares using a compass and straightedge. GSP offers more flexibility in finding the minimum area.

M8A1. Students will use algebra to represent, analyze, and solve problems.

b. Simplify and evaluate algebraic expressions.

c. Solve algebraic equations in one variable, including equations involving absolute values.

Students can let the length of AB be 1 unit. Then x can represent the length AP and 1-x can represent the length of PB. An expression can be set up for the sum of the areas:
x2 + (1-x)2

A spreadsheet can be used for different values of x until the minimum is found.