Question
Given: m || CB
Prove: m∠ABC + m∠BAC + m∠ACB = 180°
A triangle and line are shown. Line m contains points X and Y. Triangle A B C sits on line M at point A. Line m and line segment B C are parallel.
Which statement justifies that angle XAB is congruent to angle ABC?
Corresponding angles of parallel lines cut by a transversal are congruent.
Vertical angles are congruent.
Same-side interior angles of parallel lines cut by a transversal are supplementary.
Alternate interior angles of parallel lines cut by a transversal are congruent.
Prove: m∠ABC + m∠BAC + m∠ACB = 180°
A triangle and line are shown. Line m contains points X and Y. Triangle A B C sits on line M at point A. Line m and line segment B C are parallel.
Which statement justifies that angle XAB is congruent to angle ABC?
Corresponding angles of parallel lines cut by a transversal are congruent.
Vertical angles are congruent.
Same-side interior angles of parallel lines cut by a transversal are supplementary.
Alternate interior angles of parallel lines cut by a transversal are congruent.
Answers
Answered by
GPT-4o mini
The statement that justifies why angle \(XAB\) is congruent to angle \(ABC\) is:
**Corresponding angles of parallel lines cut by a transversal are congruent.**
This justification follows from the properties of parallel lines and transversals where the line segment \(AC\) serves as a transversal to the parallel lines \(m\) and \(BC\). Therefore, \(m\angle XAB\) (the angle formed by line segment \(AX\) and line \(m\)) is congruent to \(m\angle ABC\) (the angle at vertex \(B\) in triangle \(ABC\)).
**Corresponding angles of parallel lines cut by a transversal are congruent.**
This justification follows from the properties of parallel lines and transversals where the line segment \(AC\) serves as a transversal to the parallel lines \(m\) and \(BC\). Therefore, \(m\angle XAB\) (the angle formed by line segment \(AX\) and line \(m\)) is congruent to \(m\angle ABC\) (the angle at vertex \(B\) in triangle \(ABC\)).