Flashcards › Geometry justification

conditional if-then statement Angle Addition Property if angles are adjacent, then m1 + m2 = m (whole angle) complementary angle definition m1 +m2 = 90 supplementary angle definition m1 + m2 = 180 adjacent angles definition common side on the interior of angle formed by non-common sides vertical angles definition sides form two lines Linear Pair Theorem linear pair if and only if supplementary Vertical Angle Theorem vertical angles if and only if = angle measure Corresponding Angles Postulate corr. angles if and only if ll lines Parallel Lines Postulate ll lines if and only if corr. angles Parallel Lines and Slopes Theorem = slopes if and only if ll lines Transitivity of Parallelism Theorem if a ll b and b ll c, then a ll c Two Perpendiculars Theorem if two lines are perpendicular to the same line, they are parallel to each other Perpendicular to Parallels Theorem if a line is perpendicular to one of two parallels, it is perpendicular to the other perpendicular lines definition the lines form a 90 degree angle Perpendicular Lines and Slopes Theorem two lines are perpendicular if the product of their slopes is -1 Reflection Postulate reflections are 1-1 and preserve angle measure, betweenness, collinearity, and distance Figure Reflection Theorem if a figure is determined by points A, B, and C, then its reflection is determined by points A', B', and C' Perpendicular Bisector Theorem if a point is on a segment's perpendicular bisector, it is equidistant from the segment's endpoints Flip-Flop Theorem if F and F' are points/figures and r(F) = F', then r(F') = F Reflection Postulate Reflections switch orientation reflection-symmetric figure definition symmetry line if and only if reflection of F over m = F Segment Symmetry Theorem a segment has 2 symmetry lines: its perpendicular bisector and the line containing the segment Side-Switching Theorem if one side of an angle is reflected over the angle bisector, its image is the other angle side Angle Symmetry Theorem an angle's bisector is also its symmetry line Isosceles Triangle Symmetry Theorem the bisector of an isosceles triangle's vertex angle is also its symmetry line Isosceles Triangle Symmetry Corollary isosceles triangle: bisector of vertex angle, perpendicular bisector of base, and median to the base are all same line Isosceles Triangle Theorem If a triangle has two equal sides, then the opposite angles are equal Parallelogram Definition both pairs of opposite sides are parallel Rhombus Definition all four sides are equal Rectangle Definition four right angles Square Definition four right angles and four equal sides Kite Definition two distinct pairs of equal, consecutive sides Trapezoid Definition at least one pair of parallel sides Isosceles trapezoid Definiton a pair of equal base angles Kite Symmetry Theorem the line containing kite ends is also its symmetry line Kite Diagonal Theorem a kite's symmetry diagonal is the perpedicular bisector of the other diagonal and the angle bisector of the ends Rhombus Symmetry Theorem the diagonals of a rhombus are its two symmetry lines Trapezoid Angle Theorem in a trapezoid, consecutive angles between parallel sides are supplementary Trapezoid Angle Corollary In an isosceles trapezoid, base angles are equal Isosceles Trapezoid Symmetry Theorem the perpendicular bisector of a trapezoid's base also is the perpendicular bisector of the other base and its symmetry line I sosceles Trapezoid Theorem in an isosceles trapezoid, the non base sides are equal Rectangle Symmetry Theorem the perpendicular bisectors of the sides of a rectangle are its two symmetry lines If ll lines then AIA = Theorem if two lines are parallel, alternate interior angles are equal If AIA = then ll lines Theorem if alternate interior angles are equal, the lines are parallel Rhombus Theorem A rhombus is also a parallelogram Quadrilateral Hierarchy Theorem a figure is also of all the types above it on the hierarchy the definitions, postulates and theorems you need to justify conclusions