Question

select the correct answer from each drop-down menu. given: (overline{gh} cong overline{jh}) and (overline{ig} cong overline{ij}) prove: (\triangle ghi cong \triangle jhi) complete the proof. statements: (overline{gh} cong overline{jh}) and (overline{ig} cong overline{ij}); (overline{hi} cong overline{hi}); (\triangle ghi cong \triangle jhi) reasons: given; reflexive property of congruence; drop-down with sas, hl, asa, sss submit

Explanation:

Step1: 分析已知条件

已知\(\overline{GH} \cong \overline{JH}\)，\(\overline{IG} \cong \overline{IJ}\)，且\(\overline{HI}\)是两个三角形\(\triangle GHI\)和\(\triangle JHI\)的公共边，根据自反性，\(\overline{HI} \cong \overline{HI}\)。

Step2: 确定全等判定定理

三角形全等的SSS（边边边）判定定理是指如果两个三角形的三条边分别对应相等，那么这两个三角形全等。这里\(\triangle GHI\)的三边\(\overline{GH}\)、\(\overline{IG}\)、\(\overline{HI}\)分别与\(\triangle JHI\)的三边\(\overline{JH}\)、\(\overline{IJ}\)、\(\overline{HI}\)对应相等，所以符合SSS判定定理。

Answer:

SSS