SAS Criteria

Move the triangles by dragging them or point A. Rotate the triangles by moving points B and E. Use the toolbar to measure the line segments, angles or area.

Question 1

To prove triangle ABC is congruent to triangle DEF, we can do a series of rigid motions that maps DEF onto ABC. We first start by completing a translation. Which option describes the correct translation?

Point D is mapped onto point A along directed line segment DA. Point F is mapped onto point C along direct line segment FC. Point E is mapped onto point B along directed line segment EB.

Question 2

Why do we have to map D onto A and not E onto B or F onto C?

Question 3

What rigid motion should be completed following the translation?

A rotation of DEF counterclockwise about point D so that DE maps onto AB A rotation of DEF counterclockwise about point D so that DE maps onto AC

Question 4

Why does mapping DE onto AC not prove triangle congruence?

Question 5

What is the final transformation that maps DEF onto ABC and proves the two triangles are congruent?

Reflect DEF across DF, EF maps onto AC since they are congruent. Reflect DEF across EF, DE maps onto AC since they are congruent. Reflect DEF across DE, DF maps onto AC since they are congruent.

Question 6

Is there another sequence of rigid motions that would show DEF is congruent to ABC?