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Which statement proves that∠3≅∠7?

a.) If two parallel lines are cut by a transversal, the alternate interior angles are congruent.


b.) If two parallel lines are cut by a transversal, the alternate exterior angles are congruent.


c.) If two parallel lines are cut by a transversal, the corresponding angles are congruent.


d.) If two parallel lines are cut by a transversal, the vertical angles are congruent

Which statement proves that 3 7 a If two parallel lines are cut by a transversal the alternate interior angles are congruent b If two

Answer :

The correct statement that proves ∠3 ≅ ∠7 is a.) If two parallel lines are cut by a transversal, the alternate interior angles are congruent.

The correct statement that proves ∠3 ≅ ∠7 is:

  • a.) If two parallel lines are cut by a transversal, the alternate interior angles are congruent.

. According to the Theorem 19 and the properties of parallel lines, when two parallel lines are intersected by a transversal, alternate interior angles are always congruent.

In this context, ∠3 and ∠7 are alternate interior angles. Therefore, they must be congruent.

To visualize this, consider two parallel lines cut by a transversal:

  • Line 1: Parallel line
  • Line 2: Parallel line
  • Transversal: Crosses both lines
  • ∠3: Angle formed by the transversal and Line 1
  • ∠7: Corresponding angle on the opposite side of the transversal and Line 2

Since Line 1 is parallel to Line 2 and the transversal cuts across them, ∠3 and ∠7, being alternate interior angles, are congruent.

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Rewritten by : Barada

The statement that proves that ∠3 ≅ ∠7 is: C. If two parallel lines are cut by a transversal, the corresponding angles are congruent.

What is the Corresponding Angles Theorem?

If two angles lie on separate parallel lines that are crossed by a transversal and share relative corner, the angles are corresponding angles, and according to the corresponding angles theorem, both angles are congruent to each other.

Angles 3 and 7 both lie on relative corner on each parallel lines that are crossed by the transversal, therefore, both are corresponding angles

Applying the corresponding angles theorem, both angles can be proven to be congruent to each other.

Therefore, the right answer is: C. If two parallel lines are cut by a transversal, the corresponding angles are congruent.

Learn more about corresponding angles on:

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