Unit 3- Using Tools of Geometry Flashcards
duplicating a segment means
copying a segment and it’s exact length
construction
mathematical term meaning a figure is created using a compass and a straightedge
duplicating an angle means
copying and angle and it’s exact measure
segment bisector
like ray or segment in a plane that passes through the midpoint of a segment in a plane
perpendicular bisector
a segment bisector that is also perpendicular to the segment
perpendicular bisector conjecture –
if a point is on the perpendicular bisector of a segment, then it is _______ from the end points
equidistant
converse of the perpendicular bisector conjecture –
if a point is equidistant from the end points of a segment, then it is on the ______ of the segment
perpendicular bisector
constructing the perpendicular bisector also locates the _____ of a segment
midpoint
median
segment connecting the vertex of a triangle to the midpoint of its opposite side
mid-segment
segment that contains the midpoints if two sides of a triangle
distance (from point to a line)
the length of the perpendicular line segment from the point to the line
shortest distance conjecture –
the shortest distance from a point to a line is measured along the _________________ from the point to the line
perpendicular segment
altitude
a perpendicular segment from a vertex to the opposite side or to a line containing the opposite side
angle bisector conjecture –
if a point is on the bisector of an angle, then it is __________ from the sides of the angle
equidistant
converse of the angle bisector conjecture –
if a point is equidistant from the sides of an angle, then the point is on the __________ of the angle
bisector
linear pair conjecture – if two angles form a linear pair, then _______________________
the measures of the two angles add up to 180*
vertical angles conjecture – if two angles are vertical angles, _____________________________
then they have equal measures (are congruent)
transversal
a line intersecting two or more other lines in the plane
corresponding angles (CA) conjecture – if two parallel lines are cut by a transversal, then corresponding angles are ________
congruent
alternate interior angles (AIA) conjecture – if two parallel lines are cut by a transversal, then alternate interior angles are _________
congruent
alternate exterior angles (AEA) conjecture – if two parallel lines are cut by a transversal, then alternate exterior angles are _______
congruent
parallel lines conjecture – if two parallel lines are cut by a transversal, then corresponding angles are _______, alternate interior angles are _______, and alternate exterior angles are _______
congruent
slope
a constant rate of change
change in y
___________
change in x
slope intercept
y=a+bx
point slope form
y=y1+b(x-x1)
parallel lines have the same ______ but the ______ are different
slope
y intercept
perpendicular lines have ____ _____ ____
opposite reciprocal slopes
concurrent
when three or more lines meet at a single point
the point of concurrency of the angle bisectors
incenter
angle bisectors are used to find the ______ of a triangle, which can be used to _______ a circle in the triangle
incenter
inscribe
point of concurrency of the perpendicular bisectors
circumcenter
perpendicular bisectors are used to find the ______ of a triangle, which can be used to ______ a circle around the triangle
circumcenter
circumscribe
point of concurrency of the altitudes
orthocenter
point of concurrency of the medians
centroid
medians are used to find the ______ of a triangle, which divides each median into two parts so that the distance from the centroid to the vertex is _____ the distance from the centroid to the midpoint of the opposite side
centroid
twice
