54 terms

# Geometry Midterm Set 1

for geometry accelerated midterm
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postulate
a statement that is accepted as true without proof
plane
a flat surface that has no thickness
skew lines
noncoplaner lines that do not intersect and are not parallel
midpoint
a point that divides a segment into two congruent parts
two coplanar angles with a common side, a common vertex, and no common interior points
complementary angles
two angles whose measure sum to 90 degrees
supplementary angles
two angles whose measure sum to 180 degrees
perpendicular bisector
a line, segment, or ray that is perpendicular to the segment at its midpoint, thereby bisecting the segment.
angle bisector
a ray that divides an angle into two congruent coplanar angles
converse
switches the hypothesis and conclusion of a conditional statement
biconditional
made when a conditional and its converse are true; connected with "if and only if"
law of detachment
if a conditional is true and its hypothesis is true, then its conclusion is true. (if p -> q is true and p is true then q is true)
law of syllogism
if p -> q and q -> r are true statements, then p -> r is a true statement
reflexive property
a=a
symmetric property
if a=b, then b=a
transitive property
if a=b and b=c, then a=c
triangle sum theorem
the sum of the measures of the angles of a triangle is 180
triangle exterior angle theorem
the measure of each exterior angle of a triangle equals the sum of the 2 remote interior angles
scalene triangle
no congruent sides
isosceles triangle
at least 2 congruent sides
equilateral triangle
3 congruent sides
acute triangle
3 acute angles
right triangle
1 right angle
obtuse triangle
1 obtuse angle
equiangular triangle
3 congruent angles
polygon
a closed plane figure with at least 3 sides that are segments
polygon angle sum theorem
(n-2)x180
polygon exterior angle theorem
the sum of the measure of the exterior angles of a polygon, one at each vertex, is 360
cpctc
corresponding parts in congruent triangles are congruent
isosceles triangle theorem
if two sides of a triangle are congruent, then the angles opposite those sides are congruent
HL
if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and leg of another right angle, then the triangles are congruent
midsegment
a segment connecting the midpoints of two sides
midsegment theorem
if a segment joins the midpoints of 2 sides of a triangle, then the segment is parallel to the third side and half its length
altitude
a perpendicular segment from a vertex to the line containing the side opposite that vertex
median
a segment that has a vertex of a triangle and the midpoint of the opposite side as its endpoints
concurrent
when 3 or more lines intersect in one point
circumcenter
point where the perpendicular bisectors intersect; perpendicular bisectors are concurrent at this point that is equidistant from the vertices
incenter
point where the angle bisectors intersect; angle bisectors are concurrent at this point that is equidistant from the sides
centroid
the point of concurrency of the medians of a triangle
centroid theorem
the length of the segment from the vertex to the centroid is twice the length of the segment from the centroid to the midpoint
negation
the opposite truth value of a statement
inverse
negates the hypothesis and conclusion of a conditional statement
contrapositive
switches the hypothesis and conclusion and negates them both
triangle inequality theorem
the sum of the lengths of any two sides of a triangle is greater than the third side
parallelogram
a quadrilateral with both pairs of opposite sides parallel
kite
a quadrilateral with two pairs of consecutive sides congruent and no opposite sides congruent
rhombus
a parallelogram with four congruent sides
rectangle
a parallelogram with four right angles
square
a parallelogram with four congruent sides and four right angles
trapezoid
a quadrilateral with exactly one pair of opposite sides parallel
isosceles trapezoid
a trapezoid whose nonparallel sides are congruent
parallelogram properties
opposite sides are congruent, opposite angles are congruent, diagonals bisect eachother, if three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal
rhombus properties
each diagonal of a rhombus bisects two angles of the rhombus; the diagonals of a rhombus are perpendicular
rectangle property
the diagonals of a rectangle are congruent