Geometry vocab 2
Terms
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- 3 undefined terms in geometry
- point, line, plane
- space
- set of all points
- collinear
- a set of points is collinear if there is a line that contains all the points of that set.
- coplanar
- a set of points is coplanar if they are all contained in the same plane.
- Distance Postulate
- to every two different points, there corresponds a unique positive number.
- Ruler Postulate
- the points on a line can be set up in correspondence with the real numbers in such a manner that the distance between any two pointsis equal to the absolute value of the difference between the coordinates of the two points.
- Betweeness of points
- For one point to be between two other points all 3 must be different points on the same line.
- Segment Addition Postulate
- If B is between A and C, then AB+BC=AC
- Line Postulate
- For every two different points there is exactly one line that contains both points.
- Segment
- For any two points X and O the segment joining X and O is the union of X and O and all points between X and O.
- Ray
- Let A and B be two points. The ray AB is the union of AB and all points C such that B is between A and C
- Opposite Rays
- If A is between B and C, then AB and Ac are opposite rays. Opposite rays form a line.
- midpoint
- U is the midpoint of FN if U is between F and N and UF=UN
- Bisector of a segment
- Any line, segment, ray or plane that intersects a segment at its midpoint. (A bisector splits something into two equal or congruent parts.
- Angle
- The union of two non-collinear rays with a common endpoint.
- Angle Measurement Postulate
- To every angle there corresponds a measure between 0 and 180 degrees.
- Angle Addition Postulate
- If H is in the interior of angle TAM the m of angle HAT + m of angle HAM= m of angle TAM.
- Linear Pair
- If EL and EG are opposite rays and EY is any other ray, then angle YEL and angle GEy form a linear pair.
- Adjacent Angles
- Two angles are adjacent if they share a common vertex and a common side, but share no common interior points.
- Supplementary Angles
- If the sum of two angle's measures = 180 degrees then the two angles are supplementary.
- Linear Pair Postulate
- If two angles form a linear pair, then they are supplementary.
- Congruent Angles
- Two (or more) angles are congruent if they have the same measure
- Angle Bisector
- If D is in the interior of angle ABC and angle ABD is congruent to angle DBC, then ray BD is the bisector of angle ABC
- Plane Postulate
- Through any three points there is at least one plane, and through any three non-collinear points there is exactly one plane
- Flat plane Postulate
- If two points are in a plane, then the line that contains the points is also in that plane.
- Intersection of Planes Postulate
- If two planes intersect, then their intersection is a line.
- Intersection of Lines Theorem
- If two lines intersect, then they intersect at exactly one point.
- Midpoint Theorem
- If M is the midpoint of segment AB, then AM=1/2 AB and MB=1/2AB
- Angle Bisector Theorem
- If ray X is the bisector of angle ABC then m of angle ABX= 1/2 m of angle ABC and m of angle XBC=1/2 m of angle ABC
- Complementary Angles
- If the sum of the measures of 2 angles is 90 degrees, then they are complementary angles.
- Right Angle
- An angle whose measure is 90 degrees.
- Acute Angle
- An angle whose measure is less than 90 degrees.
- Obtuse Angle
- An angle whose measure is greater than 90 degrees and less than 180 degrees.
- Vertical Angles
- Two angles are vertical angles if their sides form two pairs of opposite rays.
- Vertical Angle Theorem
- Vertical angles are congruent.
- Complement Theorem
- Complements of Congruent Angles are congruent.
- Exterior sides adjacent angles theorem
- If the exterior sides of adjacent angles are perpendicular then the angles are complementary.
- Right Angle Theorem
- If two angles are right angles then they are congruent.
- Supplementary Right Angle Theorem
- If two angles are supplementary and congruent, then they are both right angles.
- Congruent Linear Pair Theorem
- If the angles in a linear pair are congruent then each is a right angle.
- Acute complementary theorem
- If two angles are complementary then both are acute angles.
- Congruent Triangles
- Two triangles are congruent if and only if their vertices can be matched up so that their corresponding parts are congruent.
- SSS Postulate
- If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
- SAS Postulate
- If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
- ASA Postulate
- If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
- CPCTC
- C orresponding P arts of C ongruent T riangles are C ongruent.
- Triangle
- If A,B and C are 3 non-collinear points, then the union of segment AB, segment BC and segment AC forms a triangle.
- Scalene Triangle
- A triangle with no congruent sides.
- Isosceles Triangle
- A triangle with two congruent sides.
- Equilateral Triangle
- A triangle with all sides congruent.
- Isosceles Triangle Theorem (I.T.T.)
- If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
- Converse Isosceles Triangle Theorem (C.I.T.T.)
- If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
- Median
- the median of a triangle is a segment from a vertexto a midpoint of the opposite side.
- Altitude
- An altitude of a triangle is the perpendicular segment from a vertex to the line that contains the opposite side.