Alternate Angles

When parallel lines are cut by a transversal, alternate angles are generated. They have different vertices and are on the opposite side of the transversal. When a transversal cuts two straight lines, the angles created on the transversal’s opposite side with respect to both lines are known as alternative angles. As a result, it’s the angles that have distinct vertices and are on opposite sides of the transversal plane.

Alternate angles are a unique type of angle in geometry. The collection of non-adjacent angles on either side of the transversal is known as alternate angles. A transversal line is formed when the straight line intersects the two or more parallel lines. Angles are generated when coplanar lines are cut by a transversal. Interior or exterior angles are the terms used to describe these angles. Two parallel lines are crossed by a transversal line to form alternate angles.

When a line crosses each other  on opposite sides of the transversal line and on opposite relative sides of the other lines, two angles are created. The alternate angles are equivalent if the two lines crossed are parallel.

Types of alternate angle:-

Alternate angles are divided into two categories: alternate interior angle and alternate exterior angle. Alternate interior angles are those that are located in the interior region of both lines. Alternate exterior angles are those that are located in the exterior region of both lines.

 1.Alternate interior angle:-

The pair of angles on the inner side of the two parallel lines but on the opposite side of the transversal are known as alternate interior angles.

  2.Alternate exterior angle:-

Alternate exterior angles are the pair of angles on the outer side of the two parallel lines but on the opposite side of the transversal.

Alternate angle Theorem:-

When a transversal cuts two parallel lines, the alternate interior angles are equal.

Proof:- Let us assume that the two parallel lines PQ and RS are cut by a transversal LM. A transversal creates the angles W, X, Y, and Z.

At the place where the straight lines PQ and LM cross,

∠W + ∠Z = 180° (the straight line is PQ)—- (1)

∠X + ∠Z = 180° (the straight line is LM)—- (2)

As a result of (1) and (2), we have

∠W = ∠X 

Again, at the place where the straight lines RS and LM intersect,

∠W +∠ Z = 180° (the straight line is RS)—- (3)

∠W +∠ Y = 180° (the straight line is LM)- (3)

As a result of (3) and (4), we have

∠Y = ∠ Z

As a result, the alternate interior angles are determined to be congruent.

As a result, it was established

Properties of alternate angle:-

• Alternate angles are congruent.
• The sum of the angles formed on the same side of the transverse on the same side of the transverse which are inside the two parallel lines are 180°.
• Alternate Angles can also be made with two non-parallel lines, although the angles generated in this way have no relationship.
• We can quickly distinguish a pair of alternate interior angles in a Z-shaped figure, Alternate Interior Angles are commonly referred to as Z-angles.
• Alternate interior angles don’t have any special qualities in the case of non-parallel lines.

Conclusion:-

Alternate angles are a unique type of angle in geometry. The set of non-adjacent angles on either side of the transversal are known as alternate angles.

When a transversal encounters coplanar lines, alternate interior angles are created. They are found on the transversal side of the parallel lines, but not on the inner side of the parallel lines. The transversal runs through both traces, which can be coplanar at different locations. Those angles determine whether or not the two supplied lines are parallel to one another. If those angles are the same, the traces that cross through the transversal are parallel.

When two parallel straight lines are intersected by a transversal, the angles formed are similar to their alternative pairings. These are known as internal angles.