Question
Question
For ΔMNO
, which statement should you verify in order to prove that the legs are congruent if the opposite angles are congruent?(1 point)
Responses
If OM¯¯¯¯¯¯¯¯¯≅ON¯¯¯¯¯¯¯¯
, then ∠O≅∠N
If line segment cap o cap m is congruent to line segment cap o cap n , then angle cap o is congruent to angle cap n
If ∠O≅∠M
, then OM¯¯¯¯¯¯¯¯¯≅ON¯¯¯¯¯¯¯¯
If angle cap o is congruent to angle cap m , then line segment cap o cap m is congruent to line segment cap o cap n
If MO¯¯¯¯¯¯¯¯¯≅MN¯¯¯¯¯¯¯¯¯¯
, then ∠N≅∠O
If line segment cap m cap o is congruent to line segment cap m cap n , then angle cap n is congruent to angle cap o
If ∠N≅∠O
, then MO¯¯¯¯¯¯¯¯¯≅MN¯¯¯¯¯¯¯¯¯¯
For ΔMNO
, which statement should you verify in order to prove that the legs are congruent if the opposite angles are congruent?(1 point)
Responses
If OM¯¯¯¯¯¯¯¯¯≅ON¯¯¯¯¯¯¯¯
, then ∠O≅∠N
If line segment cap o cap m is congruent to line segment cap o cap n , then angle cap o is congruent to angle cap n
If ∠O≅∠M
, then OM¯¯¯¯¯¯¯¯¯≅ON¯¯¯¯¯¯¯¯
If angle cap o is congruent to angle cap m , then line segment cap o cap m is congruent to line segment cap o cap n
If MO¯¯¯¯¯¯¯¯¯≅MN¯¯¯¯¯¯¯¯¯¯
, then ∠N≅∠O
If line segment cap m cap o is congruent to line segment cap m cap n , then angle cap n is congruent to angle cap o
If ∠N≅∠O
, then MO¯¯¯¯¯¯¯¯¯≅MN¯¯¯¯¯¯¯¯¯¯
Answers
Answered by
GPT-4o mini
To prove that the legs \( OM \) and \( ON \) are congruent in triangle \( \Delta MNO \) given that the opposite angles \( \angle M \) and \( \angle N \) are congruent, you should verify the following statement:
**If \( \angle M \cong \angle N \), then \( OM \cong ON \).**
This statement follows from the Angle-Side-Angle (ASA) congruence theorem or the fact that in a triangle, the sides opposite to equal angles are equal.
Thus, the correct choice would be:
**If ∠N≅∠O, then MO≅MN.**
However, this also leads to \( OM \) being congruent to \( ON \) given your triangle configuration. Thus, verifying this statement connects angle equality to side equality.
**If \( \angle M \cong \angle N \), then \( OM \cong ON \).**
This statement follows from the Angle-Side-Angle (ASA) congruence theorem or the fact that in a triangle, the sides opposite to equal angles are equal.
Thus, the correct choice would be:
**If ∠N≅∠O, then MO≅MN.**
However, this also leads to \( OM \) being congruent to \( ON \) given your triangle configuration. Thus, verifying this statement connects angle equality to side equality.