These angles are equal and are of two different types, namely alternate interior angles and alternate exterior angles. The converse of alternate exterior angles is that "if a transversal intersects two lines such that a pair of exterior angles are equal, then the two lines are parallel." What is the Alternate Angle of Angle?Īlternate angles are obtained on the opposite sides of a transversal line that have the same size. The converse of alternate interior angles is that "if a transversal intersects two lines such that a pair of interior angles are equal, then the two lines are parallel." What is the Converse of Alternate Exterior Angles Theorem? What is the Converse of Alternate Interior Angles Theorem? The measure of all pairs of alternate angles are equal. When a transversal meets two or more parallel lines, alternate interior angles formed are not supplementary angles. The angles are formed on the opposite sides of the transversal and in the interior of two lines. Yes, when a transversal meets two or more parallel lines, alternate interior angles formed are equal to each other. How Many Types of Alternate Angles are There?ĭo Alternate Interior Angles Equal Each Other? They become supplementary angles if the transversal is perpendicular to the parallel lines, hence it will make every angle equal to 90 degrees, so any two angles become supplementary angles. Do Alternate Angles Add up to 180?Īlternate angles generally don't add up to 180 degrees because they are not supplementary angles, but they can add up to 180 degrees if the transversal is perpendicular to the parallel lines. While the angles that lie on the interior of the parallel lines are not considered as the alternate exterior angles. What are Alternate Exterior Angles?Īlternate exterior angles lie on the exterior side of the parallel lines and are on the opposite side of the transversal. While the angles that lie on the exterior of the parallel lines are not considered as the alternate interior angles. ∠1=∠3 as they are vertically opposite angles.įAQs on Alternate Angles What are Alternate Interior Angles?Īlternate interior angles lie on the interior side of the parallel lines and are on the opposite side of the transversal. To prove this result, we will consider the vertically opposite angle of ∠1. We will now prove that they are congruent (i.e. In the figure above, we can observe that angles 1 and 2 is a pair of alternate exterior angle.
If two lines are parallel, then the pair alternate exterior angles formed are congruent. Similarly, we can prove that ∠2 = ∠4 Alternate Exterior Angle Theorem By alternate interior angle theorem converse, if a transversal intersects two lines such that a pair of interior angles are equal, then the two lines are parallel. What is the relation between any pair of alternate interior angles? This relation is determined by the "Alternate Interior Angle Theorem." When a transversal intersects two parallel lines, each pair of alternate interior angles are equal. Suppose two parallel lines are intersected by a transversal, as shown below: Now, let us learn about the two theorems related to Alternate Angles.
0 kommentar(er)
