Question

given: a and b are parallel and c is a transversal. prove: ∠2 ≅ ∠7 use the drop - down menus to complete the paragraph proof showing that alternate interior angles are congruent. we know that lines a and b are parallel and that line c is a transversal because that is given. we can tell that angles 2 and 5 are congruent because vertical angles are congruent. angles 5 and 7 are congruent because alternate interior angles by parallel lines cut by a transversal are congruent. therefore, angles 2 and 7 are congruent based on the drop - down menu with options: symmetric property, definition of substitution, transitive property, corresponding angles postulate.

Explanation:

Step1: Analyze the given information

We know \( \angle 2 \cong \angle 5 \) (vertical angles) and \( \angle 5 \cong \angle 7 \) (alternate interior angles). We need to find the property that allows us to conclude \( \angle 2 \cong \angle 7 \).

Step2: Recall the properties

• Symmetric property: If \( a = b \), then \( b = a \). Not applicable here.
• Definition of substitution: Replacing a quantity with its equal. But here we have a chain of congruences.
• Transitive property: If \( a \cong b \) and \( b \cong c \), then \( a \cong c \). This fits \( \angle 2 \cong \angle 5 \) and \( \angle 5 \cong \angle 7 \), so \( \angle 2 \cong \angle 7 \).
• Corresponding angles postulate: About corresponding angles, not relevant here.

Answer:

transitive property