The Converse of the Alternate Interior Angles Theorem states that if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.
The Alternate Interior Angles theorem states, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. A theorem is a proven statement or an accepted idea that has been shown to be true.
Also Know, are vertical angles congruent? When two lines intersect to make an X, angles on opposite sides of the X are called vertical angles. These angles are equal, and here’s the official theorem that tells you so. Vertical angles are congruent: If two angles are vertical angles, then they’re congruent (see the above figure).
Keeping this in consideration, what is the difference between the alternate interior postulate and its converse?
Let’s represent it in a form “if A then B”: If two lines that are cut by a transversal are parallel [Part A] then alternate interior angles formed by these lines are congruent [Part B]. Converse theorem should look like “if B then A”: So, these are two different theorems, each requiring its own proof.
What are Converse proofs?
Converse (logic) In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication P → Q, the converse is Q → P. For the categorical proposition All S are P, the converse is All P are S.
Are alternate interior angles supplementary?
When the two lines intersected by the transversal are parallel, corresponding angles are congruent, alternate interior angles are congruent, alternate exterior angles are congruent, and consecutive interior angles become supplementary, which means they have a sum of 180 degrees.
Are consecutive interior angles congruent?
Consecutive interior angles are the pairs of angles that are between two lines and on the same side of the line cutting through the two lines. The theorem states that if the two lines are parallel, then the consecutive interior angles are supplementary to each other.
What does it mean to be congruent?
Congruent. Angles are congruent when they are the same size (in degrees or radians). Sides are congruent when they are the same length.
Do alternate interior angles add up to 180?
Alternate angles form a ‘Z’ shape and are sometimes called ‘Z angles’. d and f are interior angles. These add up to 180 degrees (e and c are also interior). Any two angles that add up to 180 degrees are known as supplementary angles.
What are the supplementary angles?
Supplementary Angles. Two Angles are Supplementary when they add up to 180 degrees. These two angles (140° and 40°) are Supplementary Angles, because they add up to 180°: Notice that together they make a straight angle.
Are corresponding angles supplementary?
Two angles are said to be supplementary when the sum of the two angles is 180°. Corresponding angles are congruent. All angles that have the same position with regards to the parallel lines and the transversal are corresponding pairs e.g. 3 + 7, 4 + 8 and 2 + 6.