Proving Properties of Angles Created When Parallel Lines Are Cut by a Transversal

When two parallel lines are cut by a transversal, corresponding angles:

• Are supplementary.

• Are congruent.

• Add up to 90°.

• Are always on the same side of the transversal.

Answer explanation

When two parallel lines are cut by a transversal, the corresponding angles formed are equal in measure, making them congruent. This is a fundamental property of parallel lines and transversals.

Which of the following statements about alternate interior angles is correct?

• They are always supplementary.

• They are located on opposite sides of the transversal and inside the two lines.

• They are always equal to 90°.

• They are outside the parallel lines.

Answer explanation

The correct statement is that alternate interior angles are located on opposite sides of the transversal and inside the two lines. This is a key property in geometry, especially when dealing with parallel lines.

According to the Alternate Interior Angles Theorem:

• Alternate interior angles are supplementary.

• Alternate interior angles are congruent if the lines are parallel.

• Alternate interior angles are always equal.

• Alternate interior angles lie on the same side of the transversal.

Answer explanation

According to the Alternate Interior Angles Theorem, if two parallel lines are cut by a transversal, the alternate interior angles formed are congruent, meaning they are equal in measure.

A transversal is:

• A line that lies parallel to another line.

• A line that intersects two or more lines at different points.

• A segment that connects two points on a curve.

• A line that divides a plane into two equal halves.

Answer explanation

A transversal is defined as a line that intersects two or more lines at different points. This is the correct choice, as it accurately describes the role of a transversal in geometry.

Which of the following geometric statements justifies ∠RVM and ∠HMV are Congruent?

• If two parallel lines are intersected by a transversal, then consecutive exterior angles are complementary.

• If two parallel lines are intersected by a transversal, then alternate interior angles are congruent.

• If two parallel lines are intersected by a transversal, then alternate exterior angles are congruent.

• If two parallel lines are intersected by a transversal, then corresponding angles are complementary.

Def of Supplementary Angles

• Def of Supplementary Angles

• Def of Linear Pair

• Linear Pair Postulate

• Congruent Supplements Thm

If it is given that p ∥ q, what are ALL correct statements that can be made?

• ∠1 ≅ ∠3 by the corresponding angles postulate

• ∠2 and ∠3 are supplementary by the linear pairs postulate

• ∠1 ≅ ∠2 by the alternate exterior angles theorem

If line a is parallel to line b, then which statement is best matches the angles?

• 8x - 17 + 5x +19 = 180 because "if ll lines, then consecutive interior angles are supplementary".

• 8x - 17 = 5x + 19 because "if ll lines, then alternate interior angles are equal".

• 8x - 17 = 5x +19 because "if ll lines, then corresponding angles are equal".

If it is given that the indicated lines are parallel and that segment SF bisects ∠TSE, select ALL correct statements that could be used.

• ∠1 ≅ ∠5 by the corresponding angles postulate

• ∠2 ≅ ∠4 by the alternate interior angles theorem

• ∠1 ≅ ∠2 by the definition of an angle bisector

• ∠3 and ∠5 are supplementary by the consecutive interior angles theorem

Consecutive interior angles are:

• Always congruent.

• Angles on opposite sides of a transversal.

• Supplementary when the lines are parallel.

• Formed by the intersection of two transversals.

Answer explanation

Consecutive interior angles are supplementary when the lines are parallel, meaning they add up to 180 degrees. This is a key property in geometry related to parallel lines and transversals.