The proof of the statement m∠ABC + m∠BAC + m∠ACB = 180°, can be
used to proof that the sum of the angles in a triangle is 180°.
The statement that justifies that ∠XAB is congruent to ∠ABC is; The
alternate interior angles of parallel lines cut by a transversal are congruent.
Reasons:
Given parameters are; m║CB
Required:
To prove that m∠ABC + m∠BAC + m∠ACB = 180°
Solution;
m∠YAC ≅ m∠ACB by alternate interior angles theorem
- m∠YAC = m∠ACB by definition of congruency
m∠XAB ≅ m∠ABC by alternate interior angles theorem
- m∠XAB = m∠ABC by definition of congruency
m∠CAY + m∠XAB + m∠BAC = 180° by sum of angles on a straight line.
m∠ACB + m∠ABC + m∠BAC = 180° by transitive property of equality.
Therefore, the statement that justifies that ∠XAB is congruent to ∠ABC is
the alternate interior angles of parallel lines cut by a transversal are
congruent.
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