Question
Triangle ABC is congruent to triangle DEF.
Which statement must be true about the triangles?
Responses
AC=EF
A C equals E F
m∠B=m∠F
measure of angle B is equal to measure of angle F
m∠A=m∠D
measure of angle A is equal to measure of angle D
BC=DE
Which statement must be true about the triangles?
Responses
AC=EF
A C equals E F
m∠B=m∠F
measure of angle B is equal to measure of angle F
m∠A=m∠D
measure of angle A is equal to measure of angle D
BC=DE
Answers
Answered by
GPT-4o mini
If triangle \( ABC \) is congruent to triangle \( DEF \), then all corresponding sides and angles of the triangles are equal. This means the following statements must be true:
1. \( AC = EF \) (the side corresponding to \( AC \) in triangle \( ABC \) is \( EF \) in triangle \( DEF \))
2. \( m\angle B = m\angle F \) (the angle corresponding to \( \angle B \) in triangle \( ABC \) is \( \angle F \) in triangle \( DEF \))
3. \( m\angle A = m\angle D \) (the angle corresponding to \( \angle A \) in triangle \( ABC \) is \( \angle D \) in triangle \( DEF \))
4. \( BC = DE \) (the side corresponding to \( BC \) in triangle \( ABC \) is \( DE \) in triangle \( DEF \))
Since all these properties are true due to the congruence of the triangles, any of the statements could be an answer. However, a commonly correct statement often highlighted is \( m\angle A = m\angle D \). Thus, you can choose any of the provided statements as they are all true based on triangle congruence.
1. \( AC = EF \) (the side corresponding to \( AC \) in triangle \( ABC \) is \( EF \) in triangle \( DEF \))
2. \( m\angle B = m\angle F \) (the angle corresponding to \( \angle B \) in triangle \( ABC \) is \( \angle F \) in triangle \( DEF \))
3. \( m\angle A = m\angle D \) (the angle corresponding to \( \angle A \) in triangle \( ABC \) is \( \angle D \) in triangle \( DEF \))
4. \( BC = DE \) (the side corresponding to \( BC \) in triangle \( ABC \) is \( DE \) in triangle \( DEF \))
Since all these properties are true due to the congruence of the triangles, any of the statements could be an answer. However, a commonly correct statement often highlighted is \( m\angle A = m\angle D \). Thus, you can choose any of the provided statements as they are all true based on triangle congruence.