Triangles with Two Pairs of Congruent Angles

[size=200]Use the sliders to choose the angle measures of the blue and red angles in the triangles.[/size]

Question 1

[size=150]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)?[/size]

Question 2

[size=150]As you move the vertex, what relationships or values do not stay the same?[/size]

Question 3

[size=150]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?[/size]

Question 4

[size=150]What do you know about the angles that are not labeled in each triangle? How do you know this?[/size]

Question 5

[size=150]What can you conclude about the relationship between the two triangles themselves? [/size]

Copy and complete the following theorem based on what you discovered.

[size=150]If two ____________ of one triangle are congruent to two ________________ of another triangle, then the two triangles are ____________.[/size]

Information: Triangles with Two Pairs of Congruent Angles