ASA Exploration
Procedure
- Move points A, B and C around. Observe what happens.
- Move points A' and B' around. Observe what happens. If A' and B' behave differently than A and B, be prepared to describe how.
- If at any point the figure on the right shades in, this means you have created a triangle. Note the measurements of this new triangle and how these measures compare with the corresponding measures of the parts in ∆ABC.
- If you are able to form a triangle from the figure on the right, drag it on top of the figure on the left. Rotate it if necessary. See if the two figures can be made to overlap exactly.
- Answer the questions below.
- Once you check your answers, transfer your responses to your paper. Note: when checking answers the correct response is the highlighted one (disregard the check marks)
After you've moved points A and B of ∆ABC around, reset the sketch by pressing the reset icon in the upper right corner. This takes you back to the starting configuration. Which parts in the starting configuration of the figure on the right are congruent to parts in ∆ABC?
Which of the following statements best describes the parts you listed in the previous answer?
When the figure on the right became a triangle, how did the measure of side B'C' compare to the measure of side BC of the first triangle?
When the figure on the right became a triangle how did the measure of side A'C' compare to the measure of AC?
When the figure on the right became a triangle how die the measure of angle C' compare to the measure of angle C
Is ∆A'B'C' congruent to ∆ABC?
Which shortcut do these parts illustrate?
Is ASA a valid shortcut for determining two triangles to be congruent?