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Geometry Definition-known words used to describe a new word. 3 undefined terms (not formally defined) in Geometry: 1. Point ---has no dimension； --- represented by a dot·; --- named using one capital letter (point A = ·A). Collinear points- pts that lie on the same line. Coplanar points- pts that lie on the same plane. 2. Line --- extends forever in 1 dimension (length); --- has an arrowhead on each and representing the fact that it goes on forever. --- consists of an infinite amount of points; --- always straight; --- named with a lowercase script letter or by 2 point on the line (line AB or or line l). Skew lines- lines are not coplanar & do not intersect (line m and line l are skew lines). Parallel lines/planes ( ) – coplanar lines or planes do not intersect. (line a line b) Transversal- a line intersects 2 or more coplanar lines at different points. (Line t) Alternate interior angles- 2 interior angles lie on different parallel lines and on opposite sides of a transversal. (angle 4 & angle 6; angle 3 &angle 5) Alternate exterior angles- 2 exterior angles on opposite sides of a transversal which lie on different parallel lines. (angle 1& angle 7; angle 2& angle 8) Consecutive interior angles- 2 interior angles lie on the same side of the transversal cutting across two parallel lines. (angle 3& angle 6; angle 4&angle 5) Corresponding angles- 2 angles lie at the similar places at different lines. (angle 1& angle 5; angle2& angle6; angle3& angle7; angle4& angle8) Perpendicular lines ( ) - lines intersect to form a right angle. Perpendicular bisector- a line, segment, ray or plane that is perpendicular to a segment at its midpoint. (Line m is the bisector of segment AA’) Line perpendicular to a plane- a line intersects a plane in a point & is perpendicular to every line in the plane that intersects the line. Distance from a pt. to a line- the length of the shortest segment from a given point to a given line. (PQ is the distance from point P to line CE) 3. Plane --- extend forever in 2 dimensions (length & width); --- a flat surface consisting of infinite points; --- usually represented by a 4-side figure; ---named with a capital letter or at least 3 points on the surface of the plane ( ABC, etc). Line segment --- a section of a line that has 2 endpoints; --- named by its endpoints . Midpoint- pt bisecting a segment (point M is the midpoint of the segment). Segment bisector- a segment, ray, line or plane that intersects a segment at its midpoint (the black and red line which cross M are the segment bisector). Ray --- piece of a line with only 1 endpoint and continues forever in the other direction; --- named begins with the endpoint and a second point named on the ray (ray AB or ). Opposite rays- 2 rays that share a common initial point and face opposite direction (ray BA and ray BC are opposite rays). Angle --- 2 rays sharing the same initial point; --- named like angle BAC or BAC (vertex is always in the middle). Adjacent angle- 2 angles share common vertex & a side, but have no common interior parts. Angle bisector- a ray that divides an angle into 2 congruent adjacent angles. Types of angles 1. Acute angle- any angle which measures less than 90°. 2. Right angle- any angle which measures exactly 90°. 3. Obtuse angle- any angle which measures more than 90° but less than 180°. 4. Straight angle- any angle which measures exactly 180°. Angle Pair Relationship 1.Vertical angles- 2 angles share a common vertex & whose sides form 2 pairs of opposite rays (vertical angles are angle1&angle3; angle2&angle4). 2.Complementary angles- 2 angles whose sum is 90°. 3.Supplementary angles- 2 angles whose sum is 180°. 4.Linear pair of angles- 2 adjacent angles whose non-common sides are opposite rays. Polygon -a plane figure that is formed by 3 or more segments, is closed & no sides cross over each other. Convex- no line that contains side of a polygon goes through its interior. Concave- it is opposite of a convex. Regular polygon- equilateral & equiangular. Triangle (△)- a polygon with 3 sides. -figure formed by 3 segments joining 3 noncollinear points. Classifying by angles Classifying by sides Acute △ Scalene △ A triangle for which all 3 sides have different A △ which all interior angles are acute. lengths. Equiangular △ Equilateral △ A △ with 3 congruent angles. A △ with 3 congruent sides. Obtuse △ Isosceles △ A △ which has an obtuse angle as one of its interior angles. A △ which has an obtuse angle as one of its interior angles. Right△ (rt.△) A △ which has a right interior angle. Adjacent sides- 2 sides share a common vertex. Exterior angle- formed by extending the sides. (Angle QRS is the exterior angle) Concurrent lines- 3 or more lines, segments or rays intersect at the same point. Point of concurrency- the point at where the lines intersect. Median of a △- segment whose endpoints are a vertex of a △& the midpt. of the opposite side. Circumcenter- the point of concurrency of 3 perpendicular bisectors of the sides of △. Incenter- the point of concurrency of 3 angles bisectors. Centroid- the point of concurrency of 3 medians of a △. Circumcenter Incenter Centroid Midsegment- the segment connects the midpoints of 2 sides of a triangle. (seg.DE is the midsegment) Quadrilateral- a polygon with 4 sides. Diagonal- a segment joins 2 nonconsecutive vertices. Trapezoid- a quadrilateral has exactly 1 pair of parallel opposite sides. Isosceles trapezoid- a trapezoid has parallel legs. Parallelogram- a quadrilateral has both pairs of parallel opposite side. Rectangle- a parallelogram has 4 right angles. Kite- a quadrilateral has 2 pairs of consecutive ≌ sides but opposite sides are not ≌. Rhombus- a quadrilateral has 4 ≌ sides. Square- a quadrilateral has 4 ≌ sides & 4right angles.