IM Geo.2.5 Lesson: Points, Segments, and Zigzags

Try to prove this claim by explaining why you can be certain the claim must be true, or try to disprove this claim by explaining why the claim cannot be true. If you can find a counterexample in which the “if” part (hypothesis) is true, but the “then” part (conclusion) is false, you have disproved the claim.

 If  is a segment in the plane and  is a segment in the plane with the same length as , then  is congruent to .

“If  is a piece of string in the plane, and  is a piece of string in the plane with the same length as, then  is congruent to .”

Here are some statements about 2 zigzags. Put them in order to write a proof about figures  and .

• 1: Therefore, figure  is congruent to figure .
• 2:  must be on ray  since both  and  are on the same side of  and make the same angle with it at .
• 3: Segments  and  are the same length, so they are congruent. Therefore, there is a rigid motion that takes  to . Apply that rigid motion to figure .
• 4: Since points  and  are the same distance along the same ray from , they have to be in the same place.
• 5: If necessary, reflect the image of figure  across  to be sure the image of , which we will call , is on the same side of  as .