Short Answer
Note: Your teacher will grade your response to ensure you receive proper credit for your answers.
Given Modifying above Upper A Upper B with bar, explain how to construct a square with sides of length AB.
To construct a square with sides of length AB, follow these steps:
1. Draw segment AB to represent one side of the square.
2. Draw a point C above A and B.
3. Using segment AC, construct a right angle at C by drawing a perpendicular line from C that intersects segment AC.
4. Using segment BC, construct a right angle at C by drawing a perpendicular line from C that intersects segment BC.
5. Extend the perpendicular lines drawn in steps 3 and 4 until they intersect. Label this intersection point as D.
6. Connect points A, B, C, and D to form a quadrilateral.
7. In order to ensure that the quadrilateral is a square, it must have all sides equal in length and all angles equal to 90 degrees.
8. To verify that the quadrilateral is a square, measure the lengths of segments AD, BD, CD, and AC. If all four lengths are equal, then the quadrilateral is indeed a square.