Proving Parallel Lines and Transversals

Some windows were installed with parallel supports to prevent breaking. What is the value of x in the diagram?

Mathematical Equivalence

ON

From the diagram, the measure of angle 2 is ​ (a)   , and the measure of angle 1 is ​ (b)   .

• 57°

• 123°

• not able to be determined

• complementary

• 67°

• 113°

From the information in the diagram, what is the measure of angle 1?

• 62°

• 118°

• 28°

• not able to be determined

Answer explanation

Since we do not know if lines a and b are parallel, we do not know if the alternate interior angles are congruent.

Identify each pair of angles.

• vertical

• corresponding

• alternate exterior

• alternate interior

Match the following statement with its reason to complete the proof

• Given 

• Vertical Angles Theorem

• Transitive Property

• Converse of Corresponding Angles Theorem

• Alternate Interior Angles

• Consecutive Interior Angles

• Consecutive Exterior Angles

• Alternate Exterior Angles

• Corresponding Angles

• None

Given what we learned about parallel lines and transversals, what do we know about the angles of a trapezoid?

Which could be used to prove the lines are parallel?

• Converse of Alternate Interior Angles Theorem

• Converse of Same-Side Interior Angles Theorem

• Converse of Corresponding Angles Postulate

• Cannot be proved parallel

• No

• Yes, Corresponding angles are congruent

• Yes, Alternate Interior angles are congruent

• Yes, Alternate Exterior angles are congruent

• No

• Yes, Corresponding angles are congruent

• Yes, Alternate Interior angles are congruent

• Yes, Alternate Exterior angles are congruent