• Given two segments AB and CD which could be very far apart, how can we find out if they have the same length without measuring them individually? Do you think they have the same length? How do you check?
• For example, given a quadrilateral ABCD where all four angles at A, B, C, D are right angles, are the opposite sides AB, CD of equal length?
• Similarly, given angles ∠ AOB and ∠ A'O'B' how can we tell whether they have the same degree without having to measure each angle individually?
• For example, if two lines L and L' are parallel and they are intersected by another line, how can we tell if the angles and (as shown) have the same degree when measured?
1. Describe, intuitively, what kind of transformation will be required to move the figure on the left to each of the figures (1–3) on the right. To help with this exercise, use a transparency to copy the figure on the left. Note that you are supposed to begin by moving the left figure to each of the locations in (1), (2), and (3).
2. Given two segments and , which could be very far apart, how can we find out if they have the same length without measuring them individually? Do you think they have the same length? How do you check? In other words, why do you think we need to move things around on the plane?
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