Question

activity 2: zig then zag
construct a triangle that is congruent to your partners with the least amount of info possible.
\\(\overline{qr}\cong\overline{xy},\overline{rs}\cong\overline{yz},\angle r\cong\angle y\\)
here are some statements about 2 zigzags. put them in order to write a proof about figures qrs and xyz

• therefore, figure qrs is congruent to figure xyz
• s must be on ray yz since both s and z are on the same side of xy and make the same angle with it at y.
• segments qr and xy are the same length, so they are congruent. therefore, there is a rigid motion that takes qr to xy. apply that rigid motion to figure qrs.
• since points s and z are the same distance along the same ray from y, they have to be in the same place.
• if necessary, reflect the image of figure qrs across to be sure the image of s, which we will call s, is on the same side of xy as z

Explanation:

Step1: Start with congruent segments

Segments QR and XY are the same length, so they are congruent. Therefore, there is a rigid motion that takes QR to XY. Apply that rigid motion to figure QRS.

Step2: Adjust position of S

If necessary, reflect the image of figure QRS across to be sure the image of S, which we will call S', is on the same side of XY as Z.

Step3: Locate S' on ray YZ

S' must be on ray YZ since both S' and Z are on the same side of XY and make the same angle with it at Y.

Step4: Prove S' and Z coincide

Since points S' and Z are the same distance along the same ray from Y, they have to be in the same place.

Step5: Conclude congruence

Therefore, figure QRS is congruent to figure XYZ.

Answer:

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