Properties of Rectangles
A rectangle is a quadrilateral with four right angles. In this activity you will construct a rectangle using the definition and discover that a rectangle has many special properties besides its equal angles.
1. Construct (
).
2. Construct lines perpendicular to through points A and B. Using the 
Perpendicular Line tool, click on and A, then and B.
3. Construct point C on the line through point A.
).
2. Construct lines perpendicular to through points A and B. Using the Perpendicular Line tool, click on and A, then and B.
3. Construct point C on the line through point A.
4. Construct a line through C perpendicular to . See step 2 for help if needed.
5. Construct the fourth vertex, point D, at the intersection of this line and the line through point B. (Click the 
Point menu, then 
Intersect, then clicking on each line.)
6. Hide both lines by ctrl-clicking and un-checking Show Object from the contextual menu. Finish your rectangle by constructing the missing segments.
7. Drag different vertices of your rectangle to make sure it's constructed properly.
8. Measure the sides of the rectangle. To measure the sides, click the 
Angle menu, then choose 
Distance or Length and click on the sides.
9. Drag different vertices of your rectangle and observe the side lengths.
Point menu, then Intersect, then clicking on each line.)
6. Hide both lines by ctrl-clicking and un-checking Show Object from the contextual menu. Finish your rectangle by constructing the missing segments.
7. Drag different vertices of your rectangle to make sure it's constructed properly.
8. Measure the sides of the rectangle. To measure the sides, click the Angle menu, then choose Distance or Length and click on the sides.
9. Drag different vertices of your rectangle and observe the side lengths.Q1
Write a conjecture about the sides of a rectangle.
Q2
Is a rectangle always, sometimes, or never a parallelogram?
Q3
Explain your answer to Q2 using the tests for parallelograms from section 2.3.
10. Construct the diagonals and their point of intersection.
11. Drag parts of the rectangle and observe the diagonals. Measure lengths that look like they might be related. You can measure the distance between any two points by clicking Distance or Length, then clicking both points.
Distance or Length, then clicking both points.Q4
Write at least two conjectures about the diagonals of a rectangle.
Q5
Would each of your conjectures from Q4 also be true for a parallelogram that isn't a rectangle? Explain.
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Q5
Investigate the symmetry of the rectangle. Does it have reflection symmetry? If so, where is the line of symmetry located? Does it have rotation symmetry? If so, by what angle(s)? Where is the center of rotation located?