Question

select the correct answer from each drop - down menu.
consider $\triangle efg$ and $\triangle hij$
triangle hij is \\(
\\) triangle efg. since triangle efg uses \\(
\\) to map onto triangle hij, the triangles \\(
\\).
reset next

Explanation:

Answer:

To solve this, we analyze the triangles:

1. First Drop - Down (Triangle HJI and EFG Relationship):

• Triangle \( EFG \): Sides \( EF \) and \( FG \) have 2 tick - marks (congruent), side \( EG \) has 1 tick - mark. So it's an isosceles triangle (two congruent sides).
• Triangle \( HJI \): Sides \( HJ \) and \( JI \) have 3 tick - marks (congruent), side \( HI \) has 1 tick - mark. Also an isosceles triangle.

So Triangle \( HJI \) is congruent to triangle \( EFG \) (since they have the same side - length patterns, implying congruent triangles via SSS or similar criteria for congruence of isosceles triangles).

1. Second Drop - Down (Mapping Transformation):

Since the triangles are congruent, we can use a rigid transformation (like translation, rotation, reflection) to map \( EFG \) onto \( HJI \). Rigid transformations preserve side lengths and angles, which is necessary for congruent triangles.

(Note: If the drop - down options were, for example, "congruent to", "similar to" for the first part and "a rigid transformation", "a dilation" for the second part, the answers would be "congruent to" and "a rigid transformation" respectively.)