How can the concept of triangle congruence help explain the “rigid” property of triangles?

Before answering this question, show students the diagram on page 1.2. Tell them that the roof truss shown is the diagram is formed by a series of congruent triangles. Ask why they think the term “rigid” is used to describe a triangle. Also ask why this is a desirable property to have in construction      
and architecture. This conversation should be very informal. However, inform students that the ideas of triangle congruence explored in this activity can help explain the concept of triangle rigidness.

Have students advance to page 1.3, where they will begin investigating several different methods used to demonstrate triangle congruence.

Students should use the segments on page 1.3 to form a triangle. To manipulate the segments, students will need to grab and drag the segment itself, in addition to dragging its endpoints to rotate it. Since the lengths of the segments are locked, each student will obtain the same triangle, shown at the right.

This problem is slightly different in that students will have two triangles on their screen rather than just one. The attributes have been set so it is easy to identify which sides correspond. The given angle has been denoted a.

This problem allows students to investigate a case with two pairs of congruent corresponding angles and a congruent corresponding side.