# Geometry Midterm Review~Theorems, Postulates, Corollaries, and Laws

## 36 terms

### ruler postulate

the distance between points A and B on a line (written AB) is the absolute value of the difference between coordinates A and B when matched with real numbers on a number line
distance=length

if B is between A and C, then B + BC = AC. If AB + BC = AC, then B is between A and C.

### protractor postulate

the measure of angle AOB is equal to the absolute value of the difference between the real number for rayOA and rayOB, if rayOA and rayOB are matched to a number line between 0 and 180.

If P is in the interior of angleRST, then the measure of angleRSP and the measure of anglePST equals the measure of angleRST.

### deductive reasoning

using facts, definitions, and accepted properties, (theorems, postulates, etc.) in a logical order to write a logical argument (proof).

### law of detachment

if P implies q is true and P is true, then q must be true.

### law of syllogism

if P implies q and q implies R are true statements, then P implies R is also true. (its like the transitive property)

### inductive reasoning

making conjectures based on patterns and observations

### theorem

a statement that follows as a result of other statements; must be proven

### properties of segment congruence (2.1)

segment congruence is reflexive, symmetric, and transitive

### parallel postulate

if there is a line and a point not on the line, then there is exactly one line through the point that is parallel to the given line.

### perpendicular postulate

if there is a line and a point not on the line, then there is exactly one line through the point that is perpendicular to the given line.

### (3.1) two lines making a linear pair are perpendicular

if two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular

### (3.2) two adjacent, acute, perp. angles are complementary

If two sides of two adjacent acute angles are perpendicular, then the two angles are complementary.

### (3.3) 2 perp. lines form 4 right angles

if two lines are perpendicular, then they form four right angles.

### corresponding angles postulate

if two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

### alternate interior angles theorem

if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

### alternate exterior angles theorem

if two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

### consecutive interior angles theorem

if two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.

### perpendicular transversal theorem

if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one.

### corresponding angles converse

if two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.

### alternate interior angles converse

if two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.

### alternate exterior angles converse

if two lines are cut by a transversal so that alternate exterior angles are supplementary, then the lines are parallel.

### consecutive interior angles converse

if two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel.

### (3.11) two lines parallel to same line parallel

if two lines are parallel to the same line, then they are parallel to each other.

### (3.12) two lines perp. to same line perp.

in a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

### slope of parallel lines postulate

in a coordinate plane, two non-vertical lines are parallel if and only if they have the same slope. any vertical lines are parallel.

### slope of perpendicular lines postulate

in a coordinate plane, two non-vertical lines are perpendicular if and only if the product of their slopes is negative 1.

### triangle sum theorem (4.1)

the sum of the measures of the interior angles of a triangle measure 180 degrees.

### exterior angle theorem (4.2)

the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.

### Corollary to the triangle sum theorem (4.1)

the two acute angles of a right triangle are complementary.

### third angles theorem (4.3)

if two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent.

### side-side-side congruence postulate (SSS~4.4)

if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

### side-angle-side congruence postulate (SAS~4.5)

if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

### angle-side-angle congruence postulate (ASA~4.6)

if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

### angle-angle-side congruence theorem (AAS~4.7)

if two angles and a NON-included side of one triangle are congruent to two angles and the corresponding, non-included side of another triangle, then the two triangles are congruent.

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