Question

select the correct answer from each drop - down menu. consider △efg and △hji. triangle hji is triangle efg. since triangle efg uses to map onto triangle hji, the triangles are not congruent are congruent reset next

Explanation:

Step1: Check triangle congruence

Congruent triangles have all corresponding sides and angles equal. Here, triangle \( HJI \) and \( EFG \) are not the same in orientation and position. But we check by side - side - side (SSS) congruence.
If we assume the markings on the sides (the tick - marks) represent equal lengths. Let's say in \(\triangle EFG\), \(EF = FG=EG\) (equilateral triangle as per tick - marks) and in \(\triangle HJI\), \(HJ = JI = IH\) (equilateral triangle as per tick - marks).
Since all sides of an equilateral triangle are equal. Let the length of each side of \(\triangle EFG\) be \(a\) and of \(\triangle HJI\) be \(a\) (assuming same scale as per congruence criteria).

Step2: Determine congruence

By SSS (Side - Side - Side) congruence criterion (\(EF = HJ\), \(FG=JI\), \(EG = IH\)), \(\triangle EFG\cong\triangle HJI\). A rotation (a type of rigid transformation) can map \(\triangle EFG\) onto \(\triangle HJI\). A rigid transformation (rotation, translation, reflection) preserves the shape and size of the figure.

Answer:

Triangle \( HJI \) is a rotation of triangle \( EFG \). Since triangle \( EFG \) uses a rigid transformation (rotation) to map onto triangle \( HJI \), the triangles are congruent.