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Consider parallel lines cut by a transversal.
Parallel lines q and s are cut by transversal r. On line q where it intersects line r, 4 angles are created. Labeled clockwise, from uppercase left: angle 1, angle 2, angle 4, angle 3. On line s where it intersects line r, 4 angles are created. Labeled clockwise, from uppercase left: angle 5, angle 6, angle 8, angle 7.

Explain which theorems, definitions, or combinations of both can be used to prove that alternate exterior angles are congruent.

Respuesta :

When two parallel lines are cut by a transverse. the angles formed on the exterior of the parallel lines, on the opposite sides of the transverse are known as the Alternate Exterior Angle.

What are Alternate exterior angles?

When two parallel lines are cut by a transverse. the angles formed on the exterior of the parallel lines, on the opposite sides of the transverse are known as the Alternate Exterior Angle.

Firstly, ∠1 and ∠7 are alternate exterior angles as shown in the image, now to prove if these two angles will be congruent we can use the below proof.

First Method:

∠1  + ∠2 = 180° {Supplementary angles because both lies on the line q}

∠2 = (180° - ∠1)

Similarly, ∠2 = ∠6 = (180° - ∠1), corresponding angles are equal,

∠6 + ∠7 = 180° {Supplementary angles because both lies on the line r}

∠7 = 180° - ∠6

∠7 = 180° - (180° - ∠1)

∠7 = 180° - 180° + ∠1

∠7 = ∠1

OR

Second Method:

∠1 = ∠3 {Vertical angles formed by intersecting lines q and r}

∠3 = ∠5 {Alternate Interior angles}

∠5 = ∠7 {Vertical angles formed by intersecting lines s and r}

Learn more about the Alternate Exterior Angles:

https://brainly.com/question/14693114

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