# 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 ____________.