Step-by-step explanation:
To prove that triangle STU is congruent to triangle GHJ using the Side-Side-Side (SSS) congruence theorem, we need to show that all corresponding sides of the two triangles are congruent.
Given that segment ST is congruent to segment GH, segment TU is congruent to segment HJ, and segment SU is congruent to segment GJ, we can use a sequence of rigid motions to show that the vertices of the two triangles will line up.
Here are the missing steps in the proof:
Step 1: Translation (slide)
Translate triangle STU so that vertex S coincides with vertex G. This can be done by moving the entire triangle along a straight line without changing its orientation. After the translation, we have triangle T'U'G, where T' corresponds to T and U' corresponds to U.
Step 2: Rotation
Rotate triangle T'U'G around vertex T' so that segment T'U' aligns with segment HJ. This rotation preserves the lengths of the sides and ensures that T' and U' will align with H and J respectively. After the rotation, we have triangle T''U''G, where T'' corresponds to T' and U'' corresponds to U'.
Step 3: Translation (slide)
Finally, translate triangle T''U''G so that vertex U'' coincides with vertex J. This can be done by moving the entire triangle along a straight line without changing its orientation. After the translation, we have triangle T''U''J, where T'' corresponds to T' and U'' corresponds to U.
Now, we have triangle T''U''J, which is congruent to triangle GHJ. The corresponding sides ST and GH, TU and HJ, and SU and GJ are all congruent, satisfying the SSS congruence criterion.
By using a sequence of rigid motions (translation, rotation, translation), we have shown that triangle STU is congruent to triangle GHJ.