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Proof Cheat Sheet Name ________________________ Date ____________ Period ______ Postulate/Theorem /Property/Term Addition Property of Equality Subtraction Property of Equality Multiplication Property of Equality Division Property of Equality Substitution Property of Equality Transitive Property of Equality Transitive Property of Congruence Reflexive Property of Equality Reflexive Property of Congruence Symmetric Property of Equality Symmetric Property of Congruence ANGLES Acute Angle Obtuse Angle Right Angle Straight Angle Complementary Angles Supplementary Angles Congruent Angles Angle Bisector Vertical Angle Theorem Linear Pair Postulate Angle Addition Postulate LINES & SEGMENTS Parallel lines Perpendicular lines Congruent Segments What it states If 3x – 7 = 14 then 3x = 21 IF 5x + 5 = 10, then 5x = 5 If ½ x = 3 then x = 6 If 5x = 20, then x = 4. If a = b, then a may be replaced by b in any equation or expression. If AB + CD = EF and AB = 10, then 10 + CD = EF by substitution If a = b and b=c, then a=c. If m<1 = m<2 and m<2 = m<3, then m<1 = m<3 If a b, and b c, then a c. If m<1 m<2 and m<2 m<3, then m<1 m<3 a=a AB If a=b then b = a. AB If Segment Addition Postulate CD , then CD AB An angle whose measure is less than 90 An angle whose measure is greater than 90 but less than 180 An angle whose measure is exactly 90 An angles whose measure is exactly 180 The sum of two angle measures is 90 The sum of two angle measures is 180 Angles that have the same measure If <1 <2, then m<1 = m<2 (measures are equal) Divides an angle into two angles Vertical angles are If two angles form a linear pair, then they are a) supplementary b) sum of their measures is 180 If C is in the interior of <AOD, then m<AOC + m<COD = m<AOD Coplanar lines that do not intersect Two lines that intersect to form right angles Segments that have the same length If Midpoint Segment Bisector AB AB CD then AB = CD (lengths are equal) , Point that divides a segment into two segments A segments, ray, or line that intersects a segment at its midpoint. If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC. TRIANGLES Acute Triangle Obtuse Triangle Right Tringle Isosceles Triangle Scalene Triangle Equilateral Triangle PARALLEL LINES & ANGLE RELATIONSHIPS Corresponding Angles Postulate Corresponding Angles Converse Alternate Interior Angles Theorem Alternate Interior Angles Converse Alternate Exterior Angles Theorem Alternate Exterior Angles Converse Same-Side Interior Angles Theorem or Consecutive Interior Angles Theorem Same-Side Interior Angles Converse or Consecutive Interior Angles Converse A triangle with 3 acute angles A triangle with one obtuse angle A triangle with one right angle A triangle with at least two sides A triangle with no sides A triangle with three sides If two lines are parallel, then corresponding angles are If corresponding angles are , then the lines are parallel. If two lines are parallel, then alternate interior angles are If alternate interior angles are , then the lines are parallel. If two lines are parallel, then the alternate exterior angles are If alternate exterior angles are , then the lines are parallel. If two lines are parallel, then the same-side interior angles are supplementary. If same-side interior angles are supplementary, then the lines are parallel.