Question

identify two segments that are marked congruent to each other on the diagram below. (diagram is not to scale.)

answer attempt 1 out of 2
is congruent to

Explanation:

Step1: Analyze congruent segment markings

In geometry, congruent segments are marked with the same number of tick marks or arrows. Looking at the diagram, segment \( HE \) has three tick marks, and segment \( FG \) also has three tick marks. Alternatively, segment \( HG \) has two arrows, and segment \( EF \) also has two arrows. Also, in a rhombus (implied by congruent sides and perpendicular diagonals), diagonals bisect each other, but the tick marks/arrows here: \( HE \) and \( FG \) have the same three tick marks, so they are congruent. Or \( HG \) and \( EF \) with two arrows. Also, \( HI \) and \( FI \) (since diagonals bisect each other in a rhombus, but looking at the marks: \( HE \cong FG \) (three tick marks), \( HG \cong EF \) (two arrows), or \( EI \cong GI \), \( HI \cong FI \) (since diagonals bisect each other at right angles, so \( I \) is midpoint). But the most obvious from the marks: \( HE \) and \( FG \) (three tick marks) or \( HG \) and \( EF \) (two arrows), or \( EI \) and \( GI \), \( HI \) and \( FI \). Let's take \( HE \) and \( FG \) as an example.

Step2: Confirm congruence from markings

Segments with the same number of tick marks (or arrows) are congruent. \( HE \) has three tick marks, \( FG \) has three tick marks. So \( HE \cong FG \). Alternatively, \( HG \) (two arrows) and \( EF \) (two arrows) are congruent. Also, \( EI \) and \( GI \) (since diagonals bisect each other, \( I \) is midpoint, so \( EI = GI \)), \( HI \) and \( FI \) ( \( HI = FI \) ).

Answer:

\( HE \) is congruent to \( FG \) (or \( HG \) is congruent to \( EF \), or \( EI \) is congruent to \( GI \), or \( HI \) is congruent to \( FI \))