Study Guide Geometry
Conjecture-unproven statement that is based on observations Counterexample-an example showing a conjecture is false collinear points-points that lie on the same line coplanar points-points that lie on the same plane point-has no dimension line-extends in 1 direction plane-extends in 2 dimensions postulate/axioms-rules accepted w/o proof .
POSTULATE 2 – SEGMENT ADDITION POSTULATE. IF B IS BETWEEN A AND C THEN AB+BC=AC. IF AB+BC=AC THEN B IS BETWEEN A AND C DISTANCE FORMULA (X2-X1)2+(Y2-Y1)2 Angle-consists of 2 diff rays that have the same initial angle Sides-(rays) sides of an angle Vertex-initial part of an angle Congruent angles- angles w/ the same measure. Adjacent angle- angles that share a common vertex and side but have no common interior points Midpoint- the point that divides or Bisects-the segment into 2 congruent segments Segment Bisector- segment, ray, line, plane that intersects a segment at its midpoint MIDPONT FORMULA Vertical Angles- their sides form 2 pairs of opposite rays. Linear pair- 2 adjacent angles noncommon sides are opposite rays =180 Complementary Angles- 2= 90 Supplementary Angles- 2=180 Converse- in a condition statement is formed by switching the hypo and conclusion.
POSTULATE 5- THROUGH ANY 2 POINTS THERE EXISTS EXACTLY 1 LINE. 6- A LINE CONSISTS OF AT LEAST 2 POINTS 7-IF 2 LINES INTERSECT THEN THEIR INTERSECTION IS EXACTLY 1 POINT 8- THROUGH ANY 3 NONCOLLINEAR POINTS THERE EXISTS EXACTLY 1 PLANE 9- A PLANE CONSISTS AT LEAST 3 NONCOLLINEAR POINTS 10- IF 2 POINTS LIE IN A PLANE THEN THE LINE CONTAIING THEM LIES IN THE PLANE 11-IF 2 PLANES INTERSECT THEN THEIR INTERSECTION IS A LINE Perpendicular Lines-2 lines if they intersect to form a right angle BiConditional Statement- Contains if and only if Parallel Lines- 2 lines if they are coplanar and do not intersect Skew Lines- Lines that don’t intersect nor are coplanar
POSTULATE 2 – SEGMENT ADDITION POSTULATE. IF B IS BETWEEN A AND C THEN AB+BC=AC. IF AB+BC=AC THEN B IS BETWEEN A AND C DISTANCE FORMULA (X2-X1)2+(Y2-Y1)2 Angle-consists of 2 diff rays that have the same initial angle Sides-(rays) sides of an angle Vertex-initial part of an angle Congruent angles- angles w/ the same measure. Adjacent angle- angles that share a common vertex and side but have no common interior points Midpoint- the point that divides or Bisects-the segment into 2 congruent segments Segment Bisector- segment, ray, line, plane that intersects a segment at its midpoint MIDPONT FORMULA Vertical Angles- their sides form 2 pairs of opposite rays. Linear pair- 2 adjacent angles noncommon sides are opposite rays =180 Complementary Angles- 2= 90 Supplementary Angles- 2=180 Converse- in a condition statement is formed by switching the hypo and conclusion.
POSTULATE 5- THROUGH ANY 2 POINTS THERE EXISTS EXACTLY 1 LINE. 6- A LINE CONSISTS OF AT LEAST 2 POINTS 7-IF 2 LINES INTERSECT THEN THEIR INTERSECTION IS EXACTLY 1 POINT 8- THROUGH ANY 3 NONCOLLINEAR POINTS THERE EXISTS EXACTLY 1 PLANE 9- A PLANE CONSISTS AT LEAST 3 NONCOLLINEAR POINTS 10- IF 2 POINTS LIE IN A PLANE THEN THE LINE CONTAIING THEM LIES IN THE PLANE 11-IF 2 PLANES INTERSECT THEN THEIR INTERSECTION IS A LINE Perpendicular Lines-2 lines if they intersect to form a right angle BiConditional Statement- Contains if and only if Parallel Lines- 2 lines if they are coplanar and do not intersect Skew Lines- Lines that don’t intersect nor are coplanar