Given that lines a and b are parallel, angles 1 and 5 are congruent because they are corresponding angles, and angles 1 and 4 are congruent because they are vertical angles. Then, by which property are angles 4 and 5 congruent? Together, these statements prove which theorem? A) Transitive Property of Congruency; If parallel lines have a transversal, then supplemental angles are congruent. B) Transitive Property of Congruency; If parallel lines have a transversal, then alternate interior angles are congruent. C) Symmetric Property of Congruency; If parallel lines have a transversal, then alternate exterior angles are congruent. D) Commutative Property of Congruency; If parallel lines have a transversal, then same side interior angles are congruent.

Question

Mathematics

Moshe

12 March, 10:24

Given that lines a and b are parallel, angles 1 and 5 are congruent because they are corresponding angles, and angles 1 and 4 are congruent because they are vertical angles. Then, by which property are angles 4 and 5 congruent? Together, these statements prove which theorem? A) Transitive Property of Congruency; If parallel lines have a transversal, then supplemental angles are congruent. B) Transitive Property of Congruency; If parallel lines have a transversal, then alternate interior angles are congruent. C) Symmetric Property of Congruency; If parallel lines have a transversal, then alternate exterior angles are congruent. D) Commutative Property of Congruency; If parallel lines have a transversal, then same side interior angles are congruent.

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Answers (2)

Know the Answer?

Kaiden Wise · Answer 1

Option B)

Step-by-step explanation:

Given:

Given that lines a and b are parallel, angles 1 and 5 are congruent because they are corresponding angles, and angles 1 and 4 are congruent because they are vertical angles

To find : by which property are angles 4 and 5 congruent

Solution:

We know that if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

Also, we know that if two things are equal to the same thing then they are equal to each other. In this case, we can say that if two angles are congruent to a third angle, then they are congruent to each other. As angles 4 and 5 are both congruent to angle 1, they are congruent to each other but angles 4 and 5 are alternate interior angles. So, if parallel lines have a transversal, alternate interior angles are congruent.

Isabela Arroyo · Answer 2

Transitive Property of Congruency; If parallel lines have a transversal, then alternate interior angles are congruent.

The Transitive Property of Congruency:

If 2 angles are congruent to a third angle, then they are congruent to each other. So, since angles 4 and 5 are both congruent to angle 1, they are congruent to each other.

Angles 4 and 5 are alternate interior angles. Therefore, if parallel lines have a transversal, alternate interior angles are congruent.