Question

select all the true statements about the figure. a △fgk≅△fjk b. ∠gkh≅∠jkh c. (overline{fg}congoverline{kg}) d. ∠gfh≅∠jfh e △gkh≅△jkh f. (overline{fg}congoverline{jk})

Explanation:

Step1: Analyze congruent - triangle conditions

In \(\triangle FGK\) and \(\triangle FJK\), we have \(FG = FJ\) (marked with one - cross), \(FK=FK\) (common side), and \(GK = JK\) (marked with two - crosses). By SSS (Side - Side - Side) congruence criterion, \(\triangle FGK\cong\triangle FJK\).

Step2: Analyze angle - congruence from congruent triangles

Since \(\triangle FGK\cong\triangle FJK\), corresponding angles are congruent. Also, in \(\triangle GKH\) and \(\triangle JKH\), \(GK = JK\), \(KH=KH\) (common side), and \(GH = JH\) (marked with two - crosses). By SSS, \(\triangle GKH\cong\triangle JKH\). Then \(\angle GKH\cong\angle JKH\) and \(\angle GFH\cong\angle JFH\) (corresponding angles of congruent triangles \(\triangle FGK\) and \(\triangle FJK\)).

Step3: Analyze side - congruence statements

There is no information to suggest that \(\overline{FG}\cong\overline{KG}\) or \(\overline{FG}\cong\overline{JK}\).

Answer:

A. \(\triangle FGK\cong\triangle FJK\)
B. \(\angle GKH\cong\angle JKH\)
D. \(\angle GFH\cong\angle JFH\)
E. \(\triangle GKH\cong\triangle JKH\)