question

Postulate 1-2 Segment Addition Postulate

answer

If Q is between P and R, then PQ + QR = PR. If PQ + QR = PR then Q is between P and R.

question

The Distance Formula

answer

The distance, d, between any points with coordinate (x1, y1) and (x2, y2) is given by the following formula.

question

Definition of Midpoint

answer

The midpoint, M, of line PQ is the point P and Q such that PM = MQ.

question

Midpoint on a Number Line

answer

The coordinate of the midpoint of a line segment whose endpoints have coordinates a and b is (a+b)/2

question

Midpoint in the Coordinate Plane

answer

The coordinates of the midpoint of a line segment whose endpoints have coordinates (x1, y1) and (x2, y2) are

question

segment bisector

answer

Any segment, line, or plane that intersects a segment at its midpoint. The midpoint can also be considered a segment bisector.

question

congruent

answer

A figure can be congruent if they have the exact same size and shape.

question

Postulate 1-4 Angle Addition Postulate

answer

If R is in the interior of angle PQS, then measure of angle PQR + measure of angle RQS = measure of angle PQS. If measure of angle PQR + measure of angle RQS = measure of PQS then R is in the interior of angle PQS.

question

Definition of Right, Acute, and Obtuse Angles

answer

A right angle is an angle whose measure is 90. An acute angle is one whose measure is less than 90. An obtuse angle is one whose measure is greater than 90.

question

angle bisector

answer

Separates a segment into two congruent segments since it intersects the midpoint of the segment.

question

adjacent angles

answer

Angles in the same plane that have a common vertex and a common side, but no common interior points.

question

vertical angles

answer

Two nonadjacent angles formed by two intersecting lines.

question

linear pair

answer

Adjacent angles whose noncommon sides are opposite rays.

question

supplementary angles

answer

The sum of the measures of two angles is 180.

question

complementary angles

answer

The sum of the measures of two angles is 90.

question

perpendicular lines

answer

Two lines that intersect to form a right angle.

question

Postulate 2-1

answer

THrough any two points there is exactly one line.

question

Postulate 2-2

answer

Through any three points not on the same line there is exactly one plane.

question

Postulate 2-3

answer

A line contains at least two points.

question

Postulate 2-4

answer

A plane contains at least three points not on the same line.

question

Postulate 2-5

answer

If two points lie in a plane, then the entire line containing the two points lies in that plane.

question

Postulate 2-6

answer

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

question

Law of Detachment

answer

If p ---> q is a true conditional and p is true, then q is true.

question

Law of Syllogism

answer

If p ---> q and q ---> r are true conditionals, then p ---> r is also true.

question

Reflexive Property

answer

For every number a, a = a.

question

Symmetric Property

answer

For all numbers a and b, if a = b, then b = a.

question

Transitive Property

answer

For all numbers a, b, and c, if a = b and b = c, then a = c.

question

Addition and Subtraction Properties

answer

For all numbers a, b, and c, if a = b, then a + c = b + c and a - c = b - c.

question

Multiplication and Division Properties

answer

For all numbers a, b, and c, if a = b, then a x c = b x c, and if c does not equal 0, a/c = b/c.

question

Substitution Property

answer

For all numbers a and b, if a = b, then a may be replaced by b in any equation or expression.

question

Distributive Property

answer

For all numbers a, b, and c, a(b + c) = ab + ac.

question

Theorem 2-1

answer

Congruence of segments is reflexive, symmetric, and transitive.

question

Theorem 2-2 Supplement Theorem

answer

If two angles form a linear pair, then they are supplementary angles.

question

Theorem 2-3

answer

Congruence of angles is reflexive, symmetric, and transitive.

question

Theorem 2-4

answer

Angles supplementary to the same angle or to congruent angles are congruent.

question

Theorem 2-5

answer

Angles complementary to the same angle or to congruent angles are congruent.

question

Theorem 2-6

answer

All right angles are congruent.

question

Theorem 2-7

answer

Vertical angles are congruent.

question

Theorem 2-8

answer

Perpendicular lines intersect to form four right angles.

question

skew lines

answer

Two lines are skew if they do not intersect and are not in the same plane.

question

Postulate 3-1 Corresponding Angles Postulate

answer

If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.

question

Theorem 3-1 Alternate Interior Angle Theorem

answer

If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.

question

Theorem 3-2 Consecutive Interior Angle Theorem

answer

If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary.

question

Theorem 3-3 Alternate Exterior Angle Theorem

answer

If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent.

question

Theorem 3-4 Perpendicular Transversal Theorem

answer

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

question

Postulate 3-2

answer

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

question

Postulate 3-3 Parallel Postulate

answer

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

question

Theorem 3-5

answer

If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is congruent, then the two lines are parallel.

question

Theorem 3-6

answer

If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel.

question

Theorem 3-7

answer

If two lines in a plane are cut by a transversal so that a pair of alternate exterior angles is congruent, then the lines are parallel.

question

Theorem 3-8

answer

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

question

Definition of Slope

answer

The slope of a line containing two points with coordinates (x1, y1) and (x2, y2) is given by the formula

question

Postulate 3-4

answer

Two nonvertical lines have the same slope if and only if they are parallel.

question

Postulate 3-5

answer

Two nonvertical lines are perpendicular if and only if the product of their slopes is -1.

question

Definition of the Distance Between a Point and a Line

answer

The distance from a line to a point not on the line is the length of the segment perpendicular to the line from the point.

question

Definition of the Distance Between Parallel Lines

answer

The distance between two parallel lines is the distance between one of the lines and any point on the other line

question

Theorem 4-1 Angle Sum Theorem

answer

The sum of the measures of the angles of a triangle is 180.

question

Theorem 4-2 Third Angle Theorem

answer

If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent.

question

Theorem 4-3 Exterior Angle Theorem

answer

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

question

Corollary 4-1

answer

The acute angles of a right triangle are complementary.

question

Corollary 4-2

answer

There can be at most one right or obtuse angle in a triangle.

question

Definition of Congruence Triangles (CPCTC)

answer

Two triangles are congruent if and only if their corresponding parts are congruent.

question

Theorem 4-4

answer

Congruence of triangles is reflexive, symmetric, and transitive.

question

SSS Postulate Side-Side-Side

answer

If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.

question

SAS Postulate Side-Angle-Side

answer

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

question

ASA Postulate Angle-Side-Angle

answer

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

question

Theorem 4-5 AAS Angle-Angle-Side

answer

If two angles and a nonincluded side of one triangle are congruent to the corresponding two angles and side of a second triangle, the two triangles are congruent.

question

Theorem 4-6 Isosceles Triangle Theorem

answer

If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

question

Theorem 4-7

answer

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

question

Corollary 4-3

answer

A triangle is equilateral if and only if it is equiangular.

question

Corollary 4-4

answer

Each angle of an equilateral triangle measures 60.

Geometry H Semester 1 Final Study Guide – Flashcards

Unlock all answers in this set

Haven't found what you were looking for?

Search for samples, answers to your questions and flashcards