This Warm-up emphasizes that not every piece of information you can measure about a triangle is needed to draw it. This activity allows students to practice using the tools they will need in subsequent activities.

The goal of this discussion is for students to be clear that not every piece of given information was used to draw a unique triangle, so some information wasn’t needed to be sure that all the triangles are congruent. This discussion gives an initial opportunity to begin to connect these ideas:

• Not every piece of information you can measure about one triangle is needed to make an exact copy of that triangle.
• Not every piece of information you can measure about two triangles is needed to prove the triangles are congruent.

If needed, demonstrate how to use protractors and rulers precisely. Discuss the level of precision possible with the given tools (the triangle built with a 40-degree angle between sides that measure 5 units and 2 units actually has a third side measuring 3.699 units with angles 119.66 and 20.34 degrees). Since the goal is to write a proof without numbers, we can focus on the number of measurements needed to draw a congruent triangle, so rounding and drawings that are close enough will be just fine.

This activity gives students an opportunity to determine and request the information needed to construct a triangle congruent to the given triangle.

The Information Gap structure requires students to make sense of problems by determining what information is necessary, then to ask for information they need to solve it. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). It also allows them to refine the language they use and ask increasingly more precise questions until they get the information they need (MP6).

Monitor for students who ask for these cases, starting with cases that will always result in constructing a matching triangle and ending with those that will not:

• Angle-Side-Angle
• Side-Angle-Side 
• Side-Side-Side 
• insufficient measurements (Angle-Angle-Angle, Side-Side)

Making dynamic geometry software available gives students an opportunity to choose appropriate tools strategically (MP5).

While this activity does draw on the ambiguous Side-Side-Angle case, the main concept in the activity is that the position of the given angles and sides relative to one another matter. Students might at first think that Tyler put the sides in the wrong order relative to the given angle, which can help them see that being specific about the location of the sides and angles relative to one another matters.