Download 8th Grade Geometry Terms, Postulates and Theorems UNDEFINED

8th Grade Geometry Terms, Postulates and Theorems
UNDEFINED TERMS:
Point – no measurable length, no measurable width, no measurable depth; named
with one capital letter.
Line – measurable length, no measurable width, no measurable depth; named
with 2 capital letters (representing the names of 2 points on the line) and a symbol of a
line above the letters, or with one cursive small letter. Example: AB
Plane – measurable length, measurable width, no measurable depth; named with
3 capital letters (representing the names of 3 points not on the same line) and the word
plane in front. Example: Plane ABC
DEFINITIONS:
Collinear – points, segments or rays on the same line.
Coplanar – points, lines, segments, or rays on the same plane.
Line segment or segment – that portion of a line with 2 distinct endpoints;
Named with 2 capital letters (the names of the endpoints) and a symbol of a segment
above the letters. Example: AB
Ray – that portion of a line with 1 endpoint; named with 2 capital letters (the first
being the endpoint of the ray, and the second being a point on the ray) and a symbol of a
ray above the letters. Example: AB
Opposite Rays – Two rays that share the same endpoint and extend in opposite
directions to form a line.
Length of a Segment – a real number representing the length of a segment –
written with 2 capital letters (the names of the endpoints). Example: AB = 5 the length
of segment AB is 5 units.
Midpoint – a point that bisects a segment. If A is the midpoint of CD , then
CA = AD.
Angle – the figure created when 2 rays share the same endpoint; Named with 3
letters (the first letter is the name of a point on one side, the second letter is the name of
the shared endpoint, and the third letter is the name of a point on the other side) and an
angle sign in front of the letters or a number with the angle sign in front of the number.
Example: ABC
Sides of an angle – the two rays that form the angle.
Vertex of an angle – the shared endpoint of the 2 rays that form the angle.
Interior of an angle – the points that are between the sides of the angle.
Exterior of an angle – the points that are not in the interior or on the angle.
Measure of an angle – a real number from 0 to 180, representing the measure of
the angle using a protractor. Named with a non-capital letter m in front of the name of
the angle. Example: m ABC = 80°, the measure of angle ABC is 80 degrees.
Adjacent Angles – Two angles that share a side, and share a vertex, but do not
share any interior points.
Acute Angle – an angle that measures less than 90°.
Right Angle – an angle that measures 90°.
Obtuse Angle – an angle that measures more than 90° but less than 180°.
Straight Angle – an angle that measures 180°.
Vertical Angles – two non-adjacent angles formed when 2 lines intersect.
Complementary Angles – two angles whose measures add up to 90°.
Supplementary Angles - two angles whose measures add up to 180°.
Bisector – to cut into 2 congruent parts.
Linear Pair – 2 adjacent angles whose non-shared sides are opposite rays.
Parallel Lines – coplanar lines that do not intersect. (Symbol //)
Skew Lines – non-coplanar lines that do not intersect.
Perpendicular Lines – two coplanar lines that meet to form a right angle.
(Symbol  )
Congruent – to have the same measure.
Parallel Planes – two planes that do not intersect.
Transversal – a line that intersects 2 or more lines.
Corresponding Angles – the angles formed when 2 lines are cut by a transversal
and correspond to the same position at the points of intersection.
Alternate Interior Angles – the angles formed when 2 lines are cut by a
transversal and are between the lines, on opposite sides of the transversal and at different
points of intersection.
Alternate Exterior Angles - the angles formed when 2 lines are cut by a
transversal and are outside the lines, on opposite sides of the transversal and at different
points of intersection.
Consecutive Interior Angles - the angles formed when 2 lines are cut by a
transversal and are between the lines, on the same side of the transversal and at different
points of intersection.
Triangle – A closed figure with 3 angles and 3 sides; Named with 3 capital letters
representing the names of the vertices of the triangle and a symbol of a triangle in front of
the letters. Example: ABC
Scalene Triangle – a triangle with 3 non-congruent sides.
Isosceles Triangle – a triangle with 2 congruent sides.
Equilateral Triangle – a triangle with 3 congruent sides.
Acute Triangle – a triangle with 3 acute angles.
Right Triangle – a triangle with 1 right angle.
Obtuse Triangle – a triangle with 1 obtuse angle.
Equiangular Triangle – a triangle with 3 congruent angles.
PROPERTIES OF EQUALITY AND CONGRUENCE:
Reflexive Property of Equality: a = a
Symmetric Property of Equality: If a = b, then b = a.
Transitive Property of Equality: If a = b and b = c, then a = c.
Substitution Property of Equality: If a = b and a + c = d, then b + c = d.
Addition Property of Equality: If a = b, then a + c = b + c.
Subtraction Property of Equality: If a = b, then a - c = b - c.
Multiplication Property of Equality: If a = b, then a · c = b · c.
Division Property of Equality: If a = b, then
a b
= .
c c
Reflexive Property of Congruence: AB  AB
Symmetric Property of Congruence: If AB  CD , then CD  . AB
Transitive Property of Congruence:
If AB  CD and CD  XY , then AB  . XY
POSTULATES AND THEOREMS:
If point A is between points C and D, then AC + AD = AD.
All right angles are congruent.
If 2 angles are supplementary to the same or congruent angles, then they are
congruent to each other.
If 2 angles are complementary to the same or congruent angles, then they are
congruent to each other.
If 2 angles form a linear pair then they are supplementary. (Linear Pair
Postulate).
Vertical angles are congruent.
If 2 parallel lines are cut by a transversal, then the corresponding angles are
congruent.
If 2 parallel lines are cut by a transversal, then the alternate interior angles
are congruent.
If 2 parallel lines are cut by a transversal, then the alternate exterior angles
are congruent.
If 2 parallel lines are cut by a transversal, then the consecutive interior
angles are supplementary.
If 2 lines intersect to form a linear pair of congruent angles, then the lines are
perpendicular.
If 2 sides of 2 adjacent acute angles are perpendicular, then the angles are
complementary.
If 2 lines are perpendicular, then they intersect to form 4 right angles.
In a coordinate plane, if 2 lines are parallel, then their slopes are equal. Any
2 vertical lines are parallel.
In a coordinate plane, if 2 lines are perpendicular, then the product of their
slopes is -1. Vertical and horizontal lines are perpendicular.
If 3 parallel lines intersect 2 transversals, then they divide the transversals
proportionally.
Pythagorean Theorem
The sum of the angles of a triangle is 180°.