Questions: Not Necessarily Congruent Congruent: triangle GHI congruent to triangle square by the (Choose one) Not Necessarily Congruent Congruent: triangle ABC congruent to triangle square square by the (Choose one)

Not Necessarily Congruent Congruent: triangle GHI congruent to triangle square by the (Choose one) Not Necessarily Congruent Congruent: triangle ABC congruent to triangle square square by the (Choose one)

Transcript text: Not Necessarily Congruent Congruent: $\triangle G H I \cong \triangle$ $\square$ by the (Choose one) Not Necessarily Congruent Congruent: $\triangle A B C \cong \triangle \square$ $\square$ by the (Choose one)

Solution

Solution Steps

Step 1: Analyze the first pair of triangles.

The first pair of triangles, $\triangle GHI$ and $\triangle LKJ$, have two pairs of congruent sides ($GH \cong LK$, $HI \cong KJ$) and one pair of congruent angles ($\angle I \cong \angle J$). Since the congruent angles are not included between the congruent sides (SSA), the triangles are not necessarily congruent.

Step 2: Analyze the second pair of triangles.

The second pair of triangles, $\triangle ABC$ and $\triangle EBD$, have two pairs of congruent angles ($\angle C \cong \angle D$, $\angle B \cong \angle B$, where the latter is due to vertical angles) and one pair of congruent sides ($BC \cong BD$). Since the congruent side is included between the pair of congruent angles (ASA), the triangles are congruent.