Euclidean Geometry Exam 3

If a segment is a median,

then it is drawn from a △’s vertex to the midpoint of the side opposite the vertex

If a segment is an altitude,

then it is drawn from a △’s vertex perpendicular to the side (or extension of a side) opposite the vertex

If a segment is a △’s angle bisector,

then it is drawn from a △’s vertex to the side opposite the vertex such that it divides the vertex into two congruent angles

If a line is a segment’s perpendicular bisector,

then it is perpendicular to the segment at its midpoint

Construct an angle bisector:

(1) Construct the bisector of vertex ∠A. An angle has exactly one angle bisector. (2) Let D be the point at which the bisector intersects. Two lines intersect in at most one point

Construct a segment:

(1) Construct segment OB. 2 points determine a line

If two points are each equidistant from a segment’s endpoints,

then the line joining them is the segment’s perpendicular bisector

If a point is on a segment’s perpendicular bisector,

then it is equidistant from the segment’s endpoints

If a point is equidistant from a segment’s endpoints,

then it is on the segment’s perpendicular bisector

If two lines intersect to form congruent adjacent angles,

then the lines are perpendicular

If a segment is the angle bisector of the vertex angle of an isosceles △,

then the segment is also the median to the base, the altitude to the base, and perpendicular to the base

If a segment is the median to the base of an isosceles △,

then the segment is also the altitude to the base and the angle bisector of the vertex angle

If a segment is the altitude to the base of an isosceles △,

then the segment is also the median to the base and the angle bisector of the vertex angle

If a segment is drawn from a circle’s center to a point on the circle,

then the segment is the circle’s radius