Triangles with Two Pairs of Congruent Angles
Use the sliders to choose the angle measures of the blue and red angles in the triangles.
Question 1
Move at least one vertex of one or both of the triangles. As you move the vertex, what relationships or values are maintained (stay the same)?
Question 2
As you move the vertex, what relationships or values do not stay the same?
Question 3
Choose a new angle measure for both the blue and red angles. Move at least one vertex of one or both triangles again. Do the relationships you discovered before still hold true?
Question 4
What do you know about the angles that are not labeled in each triangle? How do you know this?
Question 5
What can you conclude about the relationship between the two triangles themselves?
Copy and complete the following theorem based on what you discovered.
If two ____________ of one triangle are congruent to two ________________ of another triangle, then the two triangles are ____________.