Question

In triangle ABC ≅ triangle EFG, which congruency statement is true?

1) BC ≅ FG
2) AB ≅ FG
3) AB ≅ EG
4) AC ≅ EF

Answer 1

The congruent sides between triangle ABC and triangle EFG are determined based on their corresponding positions. The correct congruency statement is BC ≅ FG because these sides are opposite their respective matching angles in the notation of congruent triangles.

Step-by-step explanation:

When two triangles are congruent like triangle ABC and triangle EFG, it means there is a one-to-one correspondence between their angles and their sides, and these corresponding parts are equal in measure. By the notation given, each letter in the name of the triangle corresponds to a specific angle and the side opposite to it. Therefore, you can determine which sides are congruent based on their positions within each triangle's name.

• Option 1: BC ≅ FG is true if angle B corresponds with angle F, and angle C corresponds with angle G.
• Option 2: AB ≅ FG would be incorrect because it mixes sides from different positions in the congruency statement.
• Option 3: AB ≅ EG is also incorrect for similar reasons as option 2.
• Option 4: AC ≅ EF would be incorrect because it does not match the corresponding positions in the congruency statement.

Thus, the correct congruency statement is BC ≅ FG (Option 1) because each side is opposite to the corresponding equal angles in the congruent triangles.