Midterm math study guide Flashcards
a two-dimensional pattern that you can fold to form a three dimensional figure
net
you can see the top, front, and side of an object in the same drawing
isometric drawing
shows the top view, front view, and right-side view of a three dimensional figure
orthographic drawing
indicates a location and has no size
point
a straight path that extends in two opposite directions without end and has no thickness. Infinitely many points
line
a flat surface that extends without end and has no thickness. It has infinitely many lines
plane
the part of a line that consists of two points, called endpoints, and all points between them
segment
part of a line that consists of one endpoint and all the points of the line on one side of the endpoint
ray
the set of points two or more geometric figures have in common
intersection
the distance and direction of a point from the origin of a number line
coordinate
the absolute value of the difference of the coordinates of the points
distance
the point that divides a segment into two congruent segments
midpoint
a line, segment, or ray that intersects a segment at its midpoint
segment bisector
two rays that have the same endpoint
angle
the endpoint of the two rays that form an angle
Vertex
angles that measures below 90
acute
angle that measures 90
right angle
angle that measures above 90
obtuse
angle that measures 180
straight
equal
congruent
two coplanar angles that have a common side and vertex but no common interior points
adjacent angles
two angles whose sides form two pairs of opposite rays
vertical angles
the sum of two angles equal 90
complementary angle
the sum of two angles equal 180
supplementary
a ray that divides an angle into two congruent angles
angle bisector
lines that intersect and form right angles
perpendicular lines
a line, segment, or ray that is perpendicular to the segment at its midpoint
perpendicular bisector
sum of lengths of a figure’s sides
perimeter
the amount of space a flat object takes up in squares
area
a type of reasoning that reaches conclusions based on a pattern of specific examples or past events
inductive reasoning
a conclusion reached by using inductive reasoning
conjecture
an example showing that a statement is false
counterexample
an if-then statement
conditional
the “if” in an if-then statement
hypothesis
the “then” in an if-then statement
conclusion
the opposite
negation
reversing the hypothesis and conclusion of a conditional
converse
negating the hypothesis and conclusion of a converse
contrapositive
the combination of a true conditional and its true converse. uses “if and only if”
biconditional
a=a
reflexive property
if a=b, b=a
symmetric property
If a=b and b=c, a=c
transitive property
using multiplication to distribute “a” to each term of the sum or difference within the parentheses
distributive property
two lines that lie in the same plane and do not intersect
parallel lines
lines that do not lie in the same plane and do not intersect
skew lines
a line that intersects two or more lines at distinct points
transversal
angles that lie on the same side of the transversal and in corresponding positions
corresponding angles
polygons that have corresponding sides congruent and corresponding angles congruent
congruent ploygons
the side opposite opposite the right angle in a right triangle
hypotenuse
a sequence of never-ending geometric patterns
tessallation
Theorem 2.1: Vertical Angles Theorem
vertical angels are congruent
Theorem 3.8: parallel lines
If two lines are parallel to the same line, then they are parallel to each other
Theorem 3.10: Perpendicular Transversal Theorem
In a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other
Theorem 3.11: Triangle Angle-Sum Theorem
The sum of the measures of the angles of a triangle is 180.
Theorem 4-1: Third Angles Theorem
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent
Theorem 4-2: Angle-Angle-Side Theorem
If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent
Theorem 4-3: Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent
Theorem 4-4: Converse of the Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides opposite those angles are congruent
Theorem 4-5: perpendicular bisector
If a line bisects the vertex angle of an isosceles triangle, then the line is also the perpendicular bisector of the base
Theorem 4-6: Hypotenuse-Leg Theorem
If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent
Postulate 4-1: Side-Side-Side Postulate
If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent
Postulate 4-2: Side-Angle-Side 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 two triangles are congruent
Postulate 4-3: Angle-Side-Angle Postulate
If two angles and the included side of one triangle are congruent to the two angles and the included angle of another triangle, then the two triangles are congruent.
