Question

Theorem:- the alternate angels form by a transversal of two parallel lines are of equal measures.

I need proof

Fast please

Answer 1

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When a transversal intersects two or more lines in the same plane, a series of angles are formed. Certain pairs of angles are given specific "names" based upon their locations in relation to the lines. These specific names may be used whether the lines involved are parallel or not parallel.

Let's examine these pairs of angles in relation to parallel lines:

Alternate interior angles are "interior" (between the parallel lines), and they "alternate" sides of the transversal. Notice that they are not adjacent angles (next to one another sharing a vertex).

When the lines are parallel,

the alternate interior angles

are equal in measure.

m∠1 = m∠2 and m∠3 = m∠4

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Answer 2

Step-by-step explanation:

When a transversal intersects two or more lines in the same plane, a series of angles are formed. Certain pairs of angles are given specific "names" based upon their locations in relation to the lines. These specific names may be used whether the lines involved are parallel or not parallel.

Let's examine these pairs of angles in relation to parallel lines:

Alternate interior angles are "interior" (between the parallel lines), and they "alternate" sides of the transversal. Notice that they are not adjacent angles (next to one another sharing a vertex).

When the lines are parallel,

the alternate interior angles

are equal in measure.

m∠1 = m∠2 and m∠3 = m∠4