Rectangle

Instructions

1. Introduction This activity will help you explore the properties of rectangles, focusing on diagonal lengths, congruency, and interior angles. Follow the steps below to interact with the diagram and answer the questions.
2. Exploration Steps
   • Move points A, B, and C to reshape the rectangle.
   • Check the Diagonal Lengths box. Observe whether the diagonals remain the same length as you reshape the rectangle.
   • Check the Interior Angles box to verify if the angles remain right angles.
   • Check the Side Lengths box to explore congruency between opposite sides.
3. Make a Conjecture
   • Based on your observations, make a conjecture about the diagonals of a rectangle. Use the sentence starter: "The diagonals of a rectangle are always..."
   • Test your conjecture by moving point C and rechecking the diagonal lengths.

Assessment Questions

1. Diagonal Congruency What do you notice about the diagonals of a rectangle? Select all that apply:
   • Diagonals are congruent.
   • Diagonals are always perpendicular.
   • Diagonals bisect each other.
2. Side Congruency Opposite side lengths are congruent.
   • True
   • False
3. Interior Angles Interior angles are always right angles.
   • True
   • False
4. Rectangle vs. Parallelogram What makes a parallelogram a rectangle? List two properties that rectangles have, which not all parallelograms have.
5. Application If a builder is constructing a rectangular frame and needs to check its accuracy, why might they measure the diagonals instead of the sides? Explain your reasoning.

Challenge Question Can you manipulate the rectangle so that it becomes a square? What properties change, and what stays the same? Write your answer below. Let me know if you'd like additional tweaks or specific GeoGebra formatting!