# 19 Inspirational Alternate Interior Angles Theorem Alternate Interior Angles Theorem interior angles theoremThe Alternate Interior Angles Theorem states that when two parallel lines are cut by a transversal the resulting alternate interior angles are congruent So in the figure below if k l then 2 8 and 3 5 Alternate Interior Angles Theorem interior angles htmlAlternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal

angles are the four pairs of angles that have distinct vertex points lie on opposite sides of the transversal and both angles are interior or both angles are exterior If the two angles of one pair are congruent equal in measure then the angles of each of the other pairs are also congruent Angles of a transversal Other Related theorems Alternate Interior Angles Theorem cpalms Public PreviewResourceAssessment Preview 56789Theorems include vertical angles are congruent when a transversal crosses parallel lines alternate interior angles are congruent and corresponding angles are congruent points on a perpendicular bisector of a line segment are exactly those equidistant from the segment s endpoints easycalculation Calculators TheoremsThus the converse of alternate interior angles theorem is proved Converse alternate interior angles theorem states that if two lines and a transversal form alternate interior angles that are congruent then the two lines are parallel
easycalculation Calculators TheoremsAlternate Interior Angles Theorem Proof The alternate angles theorem states that if two parallel lines are cut by a transversal then each pair of alternate interior angles are equal Alternate Interior Angles Theorem easycalculation Calculators TheoremsThus the converse of alternate interior angles theorem is proved Converse alternate interior angles theorem states that if two lines and a transversal form alternate interior angles that are congruent then the two lines are parallel exterior angles theoremThe Alternate Exterior Angles Theorem states that when two parallel lines are cut by a transversal the resulting alternate exterior angles are congruent So in the figure below if k l then

### Alternate Interior Angles Theorem Gallery geo_corresponding_angles_001_pin, image source: opossumsoft.com same side interior angles theorem n, image source: www.slideserve.com interior_angles_of_a_transversal, image source: study.com  proving lines parallel with triangle congruence, image source: mrpilarski.wordpress.com MFAS_TriangleSumProof_Image13, image source: www.cpalms.org f d%3A9c7ec17fb02a7141e2063fd5ea712f254b1356eb99032e1f7c1b5905%2BIMAGE%2BIMAGE, image source: ck12.org 10 16 2012_7 44 27_pm1350441898166, image source: www.studyblue.com tutorial_geometry2_clip_image002, image source: funmaths.com corresponding_angles, image source: pixshark.com geometry toolbox advanced proofs 3 9 638, image source: www.slideshare.net 8350050, image source: section3-1.weebly.com      