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.