Prove that alternate interior angles are congruent given that a transversal passes through two parallel lines? Transversal Line. 1. Anyone can earn In general, the measures of the interior angles of a simple convex polygon with n sides add up to (n − 2) π radians, or 180(n − 2) degrees, (2n − 4) right angles, or (n / 2 − 1) turn. Already registered? She has over 10 years of teaching experience at high school and university level. Find the value of x and the values of the two alternate interior angles. Then, since angle B and angle C are alternate interior angles, we must have that the measure of angle C is also 24 degrees. If the two lines are parallel then the alternate interior angles are congruent. A theorem is a proven statement or an accepted idea that has been shown to be true. These angles are called alternate interior angles. So, angle x = 122 then angle z = 122. 2. Alternate interior angles are formed when a transversal passes through two lines. Is it possible for the lines cut by the transversal to be parallel? Angle A and angle B form a straight angle, so A + B = 180. | Differentiated Instruction Resources, Formative Assessment in Schools | A Guide to Formative Assessment, Abnormal Psychology: Homework Help Resource, CLEP College Algebra: Study Guide & Test Prep, Principles of Physical Science: Certificate Program, CSET Social Science Subtest I (114): Practice & Study Guide, Quiz & Worksheet - Connotation & Denotation in Literature, Quiz & Worksheet - Metaphor in Literature, Quiz & Worksheet - Characteristics of Artaud's Theatre of Cruelty, Quiz & Worksheet - Spanish Practice with Common -ER and -IR Verbs, Quiz & Worksheet - Louis XIV & France's Expansion, Karl Marx & Friedrich Engels: The Communist Manifesto, California Education Technology K-12 Voucher Program for Professional Development, Finding Continuing Education Grants for Teachers, Causes & Effects of the Vietnam War: Assignment 1 - President Johnson & Guerilla Warfare, Free Online Accounting Courses with a Certificate. So the lines cannot be parallel. 37 = x. The Alternate Interior Angles theoremstates, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Use the Alternate Interior Angles Theorem to determine if the lines cut by the transversal are parallel. credit by exam that is accepted by over 1,500 colleges and universities. A straight angle, also called a flat angle, is formed by a straight line. Angle A and the original 124 degree angle are alternate interior angles and equal. Alternate Interior Angles. The Alternate Interior Angles theorem states, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Note: Alternate interior angle generally forms a z-pattern. 1. flashcard set{{course.flashcardSetCoun > 1 ? Prove: Interior alternating angles and exterior alternating angles are congruent (that is, they have the same measure of the angle.) courses that prepare you to earn Alternate interior angles create a Z. Alternate interior angles are used to prove triangles are congruent by SAS, ASA, AAS. Similarly, Angle B and 124 degrees form a straight angle, so we know that B + 124 = 180, and therefore, the measure of angle B is 56 degrees. The alternate interior angles are the angles formed when a transversal intersects two coplanar lines. Parallel lines are two lines on a two-dimensional plane that never meet or cross. 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