Unit 4 Geometry Flashcards
Midpoint formula
X one plus x two Y one plus y two
————————. ————————
2. , 2
Slope formula
Y one minus y two
—————————-
X one minus X two
Distance formula
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V ( x one - x two) + ( y one - y two)
Midpoint
Connects the midpoints of the sides of a triangle
Triangle mid segment theorem
The mid segment of a triangle is parallel to one side of the triangle and half the length
Perpendicular bisector theorem
If a point is on the perpendicular bisector line of a triangle then it is equidistant from the endpoint of that segment
Perpendicular bisector theorem converse
If a point of equidistant from the endpoints of a segment then it is the perpendicular bisector of that segment
Angle bisector theorem
If a point is on the bisector of an angle then it is equidistant from the sides of the angle
Angle bisector theorem converse
If a point is equidistant from the sides of and angle then it is on the bisector of the angle
Circumcenter
Point equidistant from all angles of a triangle ( can be outside triangle ) found by drawing perpendicular lines
Incenter
Point equidistant from all three sides of a triangle found by drawing lines from angle bisectors
Centroid
The center of gravity for a triangle also the point where all three medians meet.
Medians
Create the centroid and are are 2/3 of length on one side and 1/3 of length on other side . Also are bisector pf the lines they touch
Altitudes
Perpendicular segment from a vertex of the triangle to the line containing the opposite side also called the height . ( can be inside or outside the triangle )
Orthocenter
The point where 3 altitudes meet can be inside or outside the triangle
All triangle similarity postulates
AA
SAS
SSS or Ab ac bc
__=__=__
QR QS RS
What is needed for simularity
Same shape but not same size
So same angle measure but not same side length necessarily
Side splitter theorem
If a line is parallel to a side of a triangle and cuts through the triangle then it cuts the sides proportionally
Side splitter theorem corollary
If multiple parallel lines intersect two transversals then the segments intercepted on the transversals are proportional
Triangle angle bisector theorem
The angle bisector of a triangle cut the opposite side into pieces that are proportional to the sides of the angle
Perpendicular bisector
A perpendicular line that splits a segment in half
Angle bisector
A line the splits an angle in half
