Midterm Review Flashcards
Polygon Interior angle sum theorem
the sum of the interior angles of any polygon is 180(n - 2)
The measure of each interior angle of a regular polygon
180(n-2)/n
Polygon Exterior Angle Sum Theorem
The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.
Reflexive Property
a=a
Transitive property
If a=b and b=c, then a=c
Substitution Property
If a=b, then a can be substituted for b in any equation or expression
Verticle Angle Theorem (VAT)
Vertical angles are congruent
Complimentary angles
two angles that add up to 90 degrees
supplementary angles
Two angles whose sum is 180 degrees
Congruent Supplements Theorem
If two angles are supplementary to the same angle (or to two congruent angles), then the two angles are congruent.
Congruent Complements Theorem
If two angles are complementary to the same angle (or to congruent angles), then they are congruent.
Linear Pair Theorem
If two angles form a linear pair, then they are supplementary
if two angles are congruent and supplementary…
then each is a right angle
all right angles are…
congruent
rigid motion
A transformation that preserves distance and angle measures
isosceles triangle theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
CPCTC
corresponding parts of congruent triangles are congruent
congruence criterion (proving triangle congruence)
ASA, AAS, SAS, SSS, HL
colinear
3 or more points that lie on the same line
Coplaner
points that lie on the same plane
Segment Addition Postulate
If B is between A and C, then AB + BC = AC
Angle Addition Postulate
The sum of the measure of two adjacent angles is equal to the measure of the angle formed by the non-common sides of the two adjacent angles.
construction
A geometric drawing that uses a limited set of tools, usually a compass and straightedge.
Perpedicular Bisector
a segment, ray, line, or plane that is perpendicular to a segment at its midpoint
midpoint formula
(x₁+x₂)/2, (y₁+y₂)/2
distance formula
d = √[( x₂ - x₁)² + (y₂ - y₁)²]
conjecture
reasoning that reaches conclusions based on a pattern of specific examples or past events
counterexample
an example that satisfies the statements conditions but does not lead to the statements conclusions
conditional statement
a statement that can be written in if-then form, with a hypothesis and a conclusion (if p then q)
converse
the statement formed by exchanging the hypothesis and conclusion of a conditional statement (if q then p)
negation
the opposite of the original statement. (not P)
Inverse
Negating both the hypothesis and conclusion of a conditional statement. (if not p then not q)
Contraposative
Negating and reversing both hypothesis and conclusion (If not q, then not p)
biconditional statement
A statement that contains the phrase “p if and only if q”
Law of Detachment
If a conditional is true and its hypothesis is true, then its conclusion is true.
Law of Syllogism
If p–>q and q–>r are true statements, then p–>r is a true statement.
same side interior angle postulate
If two parallel lines are cut by a transversal, then same-side interior angles are supplementary.
alternate interior angle theorem
If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.
corresponding angle theorem
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent
alternate exterior angle theorem
If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent.
Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle is 180 degrees
exterior angle theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.
Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
circumscribed
A circle that contains all the vertices of a polygon
inscribed
A polygon is inscribed in a circle if each of its vertices lie on the circle
altitude
a perpendicular segment from a vertex to the line containing the opposite side
median
a segment that has endpoints at a vertex and a midpoint of a side opposite the vertex
the largest angle is opposite…
the longest side
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
reflections
Transformation that reflects each point in the preimage across a line of reflection to the image
translation
A transformation that moves every point of a figure the same distance in the same direction
composition of rigid motions
a transformation with two or more rigid motions in which the second rigid motion is performed on the image of the first rigid motion
rotation
transformation that rotates each point in the preimage around a point called the center of a rotation by an angle measure called the angle of rotation
glide reflection
a reflection followed by a translation in a direction parallel to the line of reflection
line of symmetry
a line that divides a figure into two halves that are mirror images of each other
Point symmetry
a rotation of 180 degrees that maps the figure onto itself
