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Teacher Geometry Notes 2.3 Segment and Angle Relationships Vocabulary: (1) Congruent (a) Two segments are congruent, Μ Μ Μ Μ π΄π΅ β Μ Μ Μ Μ πΆπ·, if they have the same length. (b) Two angles are congruent, β’π β β’π, if they have the same measure. I (2) The midpoint of a segment is the point that divides the segment into two congruent segments. (3) A segment bisector is a segment, ray, line or plane that intersects a segment at its midpoint. (4) An angle bisector is a ray that divides the angle into two congruent angles. (5) Perpendicular I (a) Two lines are perpendicular (β₯) if they intersect to form a right angle. (b) A line is β₯to a plane if it is β₯ to each line in the plane that intersects it. I ***Definitions β can always be interpreted βforwardβ and βbackwardβ*** i.e. β βIf two segments have the same measure, then they are β .β AND βIf two segments are β then they have the same measureβ The Distance Formula β used to compute the distance between points in a coordinate plane. (a) Let π΄ = (π₯1 , π¦1 ) and π΅ = (π₯2 , π¦2 ) be points on a coordinate plane. The distance between A and B is: π΄π΅ = β(π₯2 β π₯1 )2 + (π¦2 β π¦1 )2 (E1.) Find the distance between (β1,2)πππ (2, β4). π΄π΅ = β(2 β β1)2 + (β4 β 2)2 = β32 + (β6)2 = β9 + 36 = β45 = 3β5 (P1.) Find the distance between (0, 4)πππ (2, 3). π΄π΅ = β(2 β 0)2 + (3 β 4)2 = β22 + (β1)2 = β4 + 1 = β5