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### Angle Addition Postulate

the sum of the measures of adjacent angles equals the measure of the larger angle they form together

### The Parallel Postulate

Through any point not on a given line, there exists exactly one line parallel to the given line. (Given a line and a point not on that line, there exists exactly one line that can be drawn through that point, parallel to the given line).

### If a line

ray or segment divides a segment into two congruent segments, then it bisects the segment.

### If two triangles are congruent

then all pairs of corresponding sides and corresponding angles are congruent.

### If a segment is a median of a triangle

then it drawn from a vertex to the midpoint of the opposite side.

### If a segment is drawn from a vertex of a triangle to the midpoint of the opposite side

then it is a median.

### If a segment is a median of a triangle

then it divides the side of the triangle that it intersects into two congruent segments.

### If a segment drawn from a triangle's vertex divides the opposite side into 2 congruent segments

then it is a median.

### If a segment is an altitude of a triangle

then it is drawn from a vertex perpendicular to the opposite side (the side of the triangle which it intersects)

### If a segment is drawn from a vertex of a triangle perpendicular to the opposite side

then it is an altitude.

### If a segment is drawn from a vertex forming right angles with the opposite side

then it is an altitude.

### If a quad is a rhombus

then it is a parallelogram in which at least one pair of consecutive sides is congruent

### If a quad is an isosceles trapezoid

then it is a trapezoid with congruent legs (it has exactly one pair of parallel bases and congruent legs)

### If congruent segments are subtracted from congruent segments

then the resulting segments are congruent

### If two points are each equidistant from the endpoints of a segment

then they determine the perpendicular bisector of that segment

### If a point is on the perpendicular bisector of a segment

then it is equidistant from the endpoints of that segment

### If a point is equidistant from the endpoints of a segment

then it LIES ON the perpendicular bisector of that segment

### the measure of either of the remote interior angles

The measure of an exterior angle of a triangle is greater than

### If two lines are cut by a transversal such that a pair of alternate interior angles are congruent

then the lines are parallel

### If two lines are cut by a transversal such that a pair of alternate exterior angles are congruent

then the lines are parallel

### If two lines are cut by a transversal such that a pair of corresponding angles are congruent

then the lines are parallel

### If two lines are cut by a transversal such that a pair of same side interior angles are supplementary

then the lines are parallel

### If two lines are cut by a transversal such that a pair of same side exterior angles are supplementary

then the lines are parallel

### In a plane if a line is perpendicular to one of 2 parallel lines,

then it is perpendicular to the other

### In a plane if a line is perpendicular to one of 2 parallel lines

then it is perpendicular to the other