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// Lines, ∠ngles, & Tri∆ngles GEOMETRY Transversals (corr. ∠ ‘s) Name AIA Corresponding Angles Def. are angles in the same relative locations to the transversal line (i.e. upper right, lower left, lower right, upper left etc.) Picture Corresponding Angles Postulate/Thm. ll lines ⇔ ≅ corr. ∠’s Lines are parallel if and only if corresponding angles are congruent. Theorem ll lines ⇔ ≅ A.I.A. Alternate Interior Angles are congruent if and only if lines are parallel. Alternate Interior Angles AEA ll lines ⇔ ≅ A.E.A. Alternate Exterior Angles are congruent if and only if lines are parallel. Alternate Exterior Angles SSI Unique Perpendicular Line Through a point not on a line, there is exactly one perpendicular line. ll lines ⇔ S.S.I ∠’s = 180°. Same-Side Interior Angles are supplementary if and only if lines are parallel. SameSide Interior SSE ll lines ⇔ S.S.E ∠’s = 180°. Same-Side Exterior Angles are supplementary if and only if lines are parallel. SameSide Exterior Perpendicular to Parallels Thm. ⊥ l & l // p ⇒ t ⊥ p t Two Perpendiculars Thm. t l If a line is perpendicular to one of two parallel lines, then it is also perpendicular to the second line. TRIANGLE THEOREMS p POLYGONS 2 3 Unique Parallel Line Through a point not on a line, there is exactly one parallel line. 1 4 int. ∠ t ⊥ l & t ⊥ p ⇒ l // p If two lines are perpendicular to the same line in the same plane, then they are parallel to each other. Interior Angle Sum = 180 (n–2) Interior Angle Measure = 180 (n–2) n ext. ∠ Triangle Sum Theorem m∠1 + m∠2 + m∠3 = 180° Exterior Angle Sum = 360° Exterior Angle Theorem m∠4 = m∠2 + m∠3 Exterior Angle Measure = 360÷n Central Angle = 360°÷n r p l Parallel Transitivity (3 //’s) Thm. r // p & p // l ⇒ r // l If two lines are parallel to a third line, then they are parallel to each other.