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Postulates
Theorems
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Additional!
100
If two angles form a linear pair, then they are supplementary.
What is linear pair postulate?
100
Segments/angles are congruent.
What is congruence of segments/angles?
100
If two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.
What is corresponding angles converse?
100
If two lines are cut by a transversal so the alternatre interior/exterior angles are congruent, then the lines are parallel.
What is alternate interior/exterior angles converse?
100
Two lines do not intersect and are not coplaner.
What is a skew line?
200
Vertical angles are congruent.
What is vertical angles congruence theorem?
200
All right angles are congruent.
What is right angles congruence theorem?
200
In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.
What is lines perpendicular to a transversal theorem?
200
If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel.
What is consecutive interior angles converse?
200
They have corresponding positions.
What is corresponding angles?
300
If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.
What is parallel postulate?
300
If two angles are supplementary to the same angle (or to congruent angles), then they are congruent.
What is congruent supplements theorem?
300

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

What is the Triangle Inequality Theorem

300
If two lines are parallel to the same line, then they are parallel to each other.
What is transitive property of parallel lines?
300
They lie between the two lines and on the same side of the transversal.
What is consecutive interior angles?
400
If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.
What is perpendicular postulate?
400
If two angles are complementary to the same angle (or to congruent angles), then they are congruent.
What is congruent complements theorem?
400

If two lines intersect, then their intersection is exactly one point.

What is the Line Intersection Postulate?

400
If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
What is theorem 3.8?
400
If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.
What is theorem 3.10?
500
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
What is corresponding angles postulate?
500
If two lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.
What is consecutive interior angles theorem?
500

The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.

What is the Arc Addition Postulate?

500
If two lines are perpendicular, then they intersect to form four right angles.
What is theorem 3.9?
500
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.
What is perpendicular transversal theorem?
600

If two planes intersect, then their intersection is a line.

What is the Plane Intersection Postulate?

600

If three parallel lines intersect two transversals, they divide them proportionally.

What is the Three Parallel Lines Theorem?

600

In the same circle or congruent circles, two chords are congruent if and only if they are equidistant from the center.

What is the Equidistant Chords Theorem?

600

For any triangle ABC, where c is the length of the longest side, the following statements are true.

 If c^2<a^2+b^2, then triangle ABC is acute. 

If c^2>a^2+b^2, then triangle ABC is obtuse.

What is the Pythagorean Inequalities Theorem?

600

The product of their slopes is -1.

What is the slopes of perpendicular lines?