Flashcards › Justifications in geometry

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