Test Android StudyStack App

Please help StudyStack get a grant! Vote here.

Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.

Normal Size Small Size show me how

Normal Size Small Size show me how

Question | Answer |
---|---|

Point | Has no dimension. Represented by a dot. Named using a capital letter. |

Line | One dimensional. A set of points that extend infinitely in two opposite directions. Straight. Named using two labeled points or one lowercase letter. |

Plane | A two dimensional flat surface that extends infinitely in two directions. Represented by a four sided figure. Named using 3-4 points or a capital letter that is not a point. |

Collinear Points | 3 or more points on the same line |

Coplanar Points | Points that lie in the same plain |

Line segment | Part of a line that has two end points. Named by its two end points. |

Ray | Part of a line. One endpoint that extends infinitely in one direction. Named by its end point and one other point. |

Opposite Rays | Two rays that share a common end point that extends infinitely in opposite directions. |

Postulate/Axiom | A statement that is accepted to be true without proof. |

Ruler Postulate | Given line AB. AB = |B-A| |

Equality System | System that compares size using measurements. |

Congruence System | System that compares parts to show that figures are the same size and/or shape. |

Segment Addition Post | Given segment AC with midpoint B. AB + BC = AC. |

Distance Formula | States that distance between two points can be found by taking the square root of the difference of the x coordinates squared added to the difference of the y coordinates squared. |

Angle | A geometric figure that consists of two rays (sides) that meet at a common point (vertex). Usually named by its vertex. |

Vertex | The common point of an angle. |

Protractor Postulate | States that when using a protractor, you should put the vertex at 0/180 and then subtract the two numbers that the sides touch to get the measure of the angle. |

Angle Addition Postulate | States that you can add the parts of an angle to get the whole angle. |

Acute Angle | An angle that is less than 90 degrees. |

Right Angle | An angle that is 90 degrees. |

Obtuse Angle | An angle that is more than 90 degrees but less than 180 degrees. |

Straight Angle | An angle that is 180 degrees. |

Adjacent Angles | A pair of angles that share the same vertex and a common side. |

Bisect | To cut into to equal parts. |

Midpoint | The point that divides a segment into two equal segments. |

Segment Bisector | A segment that passes through the midpoint of another segment. |

Angle Bisector | A ray that divides an angle into two equal angles. |

The Midpoint Formula | States that you can find the midpoint of a segment in the following way. X coordinate: add the two x coordinates and divide them by 2. Y coordinate: add the two y coordinates and divide them by two. |

Complementary Angles | A pair of angles that add up to 90 degrees. May or may not be adjacent. |

Supplementary Angles | A pair of angles that add up to 180 degrees. May or may not be adjacent. |

Linear Pair | Pair of angles that form a straight angle. Must be adjacent. AKA Adjacent supplementary angles. |

Vertical Angles | A pair of angles that are across (opposite) from each other that have the same vertex. Never adjacent. Always equal. |

Perpendicular Lines | Coplanar lines that intersect to form right angles. |

Line Perpendicular to a Plane | A line that intersects the plane in a point and is perpendicular to every line in the plane that intersects it. |

Biconditional Statement | A statement that contains the phrase if and only if. (p if and only if q) |

Conditional Statement | A type of logical statement that has two parts, a hypothesis and a conclusion. (p then q) |

Converse | The statement formed by switching the hypothesis and conclusion of a conditional statement. (q then p) |

Negation | The negative of a statement. Represented by ~. |

Inverse | The statement formed when you negate the hypothesis and conclusion of a conditional statement. (~p then ~q) |

Contrapositive | The statement formed when you negate the hypothesis and conclusion of the converse of a conditional statement. (~q then ~p) |

Deductive Reasoning | Uses fact, definitions, and accepted properties in a logical order to write a logical argument. |

Inductive Reasoning | Uses patterns and observations to form a conjecture. |

Conjecture | An unproven statement |

The Law of Detachment | If p --> q is a true conditional statement and p is true, then q is true. |

The Law of Syllogism | If p --> q and q --> r are true conditional statements, then p --> r is true. |

Addition Property of Equality | If a=b, then a+c=b+c |

Subtraction Property of Equality | If a=b, then a-c=b-c |

Multiplication Property of Equality | If a=b, then ac=bc |

Division Property of Equality | If a=b, then a/c=b/c |

Distributive Property of Equality | a(b+c)=ab+ac |

Reflexive Property of Equality | For any real number a, a=a |

Symmetric Property of Equality | If a=b, then b=a |

Transitive Property of Equality | If a=b and b=c, then a=c |

Substitution Property of Equality | If a=b, then a can be substituted for b in any equation or expression. |

Reflexive Property of Segment Congruence | For any segment AB, AB is congruent to AB. |

Symmetric Property of Segment Congruence | If AB is congruent to CD, then CD is congruent to AB. |

Transitive Property of Segment Congruence | If AB is congruent to CD, and CD is congruent to EF, then AB is congruent to EF. |

Reflexive Property of Angle Congruence | For any angle A, angle A is congruent to anlge A. |

Symmetric Property of Angle Congruence | If angle A is congruent to angle B, then angle B is congruent to angle A. |

Transitive Property of Angle Congruence | If angle A is congruent to angle B, and angle B is congruent to angle C, then angle A is congruent to angle C. |

Right Angle Congruence Theorem | All right angles are congruent. |

Congruent Supplements Theorem | If two angles are supplementary to the same angle then they are congruent. |

Congruent Compliments Theorem | If two angle are complimentary to the same angle then they are congruent. |

Linear Pair Postulate | If two angles form a linear pair, then they are supplementary. |

Vertical Angles Theorem | All vertical angles are congruent. |

Parallel Lines | Coplanar lines that do not intersect. |

Skew Lines | Lines that do not intersect and are not coplanar. |

Parallel Planes | Planes that do not intersect. |

Parallel Postulate | 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. |

Perpendicular Postulate | 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. |

Transversal | A line that intersects two or more coplanar lines at different points. |

Interior Angles | Inside Angles |

Exterior Angles | Outside Angles |

Corresponding Angles | Two angles that occupy corresponding positions. They are always on the same side of the transversal. |

Alternate Exterior Angles | Two angles that are exterior and cross over the transversal. |

Alternate Interior Angles | Two angles that are interior and cross over the transversal. (Z shaped) |

Consecutive Interior Angles | Two interior angles that are on the same side of the transversal. (Same side interior) |

Hypothesis | If part of a conditional statement. |

Conclusion | Then part of a conditional statement. |

Through any two points there exists exactly one line. | Postulate 5 |

A line contains at least two points. | Postulate 6 |

If two lines intersect, then their intersection is exactly one point. | Postulate 7 |

Through any three noncollinear there exists exactly one plane. | Postulate 8 |

A plane consists of at least three noncollinear points. | Postulate 9 |

If two points lie in a plane, then the line containing them lies in the plane. | Postulate 10 |

If two plans intersect, then their intersection is a line. | Postulate 11 |

Equivalent Statements | Two statements that are both true or both false. |

Two-Column Proof | Has numbered statements and reasons that show the logical order of an argument. |

If two lines intersect to form a linear pair of con ground angles, then the line perpendicular. | Theorem 3.1 |

If two sides of two adjacent acute angels are perpendicular, then the angles are complimentary. | Theorem 3.2 |

If two lines are perpendicular, then they intersect to form four right angles. | Theorem 3.3 |

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. |

Consecutive Interior Angles Theorem | If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. |

Alternate Exterior Angles Theorem | If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. |

Perpendicular Transversal Theorem | If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other. |

Corresponding Angles Converse Postulate | If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. |

Alternate Interior Angles Converse Theorem | If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel. |

Consecutive Interior Angles Converse Theorem | If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel. |

Alternate Exterior Angles Converse Theorem | If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel. |

If two lines are parallel to the same line, then they are parallel to each other. | Theorem 3.11 |

In a plane, if two line are perpendicular to the same line, then they are parallel to each other. | Theorem 3.12 |

Slopes of Parallel Lines Postulate | In a coordinate, two nonvertical lines are parallel if and only if they have the same slope. Any two vertical lines are parallel. |

Slope Intercept Form | y=mx+b |

Slope Formula | m=change in y/change in x |

Rule of Parallel Lines | Two parallel lines must have the same slope but different y-intercepts. |

Slopes of Perpendicular Lines Postulate | In a coordinate plane, two nonvertical lines are perpendicular only if the product of their slopes are -1 or negative reciprocals. |

Triangle | A figure formed by three segments joining three noncollinear points. |

Equilateral Triangle | A triangle with 3 congruent sides |

Isosceles Triangle | A triangle with at least 2 congruent sides |

Scalene Triangle | A triangle with no congruent sides |

Acute Triangle | A triangle with 3 acute angles |

Equiangular Triangle | A triangle with 3 congruent angles |

Right Triangle | A triangle with 1 right angle |

Obtuse Triangle | A triangle with 1 obtuse angle |

Triangle Sum Theorem | The sum of the measures of the interior angles of a triangle is 180 degrees. |

Exterior Angle of a Triangle Theorem | The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. |

Corollary to a Theorem | A statement that can be proved easily using a theorem. |

Congruence Statement | A statement that shows two triangles are congruent to each other. |

Third Angle Theorem | If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. |

SSS Congruence Postulate | If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. |

SAS Congruence Postulate | If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. |

ASA Congruence Postulate | If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent. |

AAS Congruence Theorem | If two angles and a nonincluded side of one triangle are congruent to two angles and a non included sife of a second triangle, then the two triangles are congruent. |

Corresponding Parts of Congruent Triangles are Congruent | CPCTC |

Base Angles | The two angles adjacent to the base of an isosceles triangle. |

Vertex Angles | The angle opposite the base in an isosceles triangle. |

Base Angles Theorem (Isosceles Triangle Theorem) | If two sides of a triangle are congruent, then the opposite them are congruent. |

Base Angles Converse Theorem | If two angles of a triangle are congruent then the sides opposite them are congruent. |

Corollary to the Base Angles Theorem | If a triangle is equilateral, then it is equiangular. |

Corollary to the Base Angles Converse Theorem | If a triangle is equiangular, then it is equilateral. |

Hypotenuse Leg Congruence Theorem | If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the triangles are congruent. |

Perpendicular Bisector | A segment, ray, line, or plane that is perpendicular to a segment at its midpoint. |

Equidistant | Same distance |

Distance from a Point to a Line | The length of the perpendicular segment form the point to the line. |

Perpendicular Bisector Theorem | If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of a segment. |

Perpendicular Bisector Converse Theorem | If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. |

Angle Bisector Theorem | If a point is on the angle bisector of an angle, then it is equidistant from the sides of the angle. |

Angle Bisector Converse Theorem | If a point in the interior of an angle and is equidistant from the sides of the angle, then it lies on the bisector of the angle. |

Perpendicular Bisector of a Triangle | A line that is perpendicular to a side of a triangle at the midpoint of the side. |

Concurrent Lines | Three or more lines that meet at the same point. |

Point of Concurrency | The point of intersection of concurrent lines. |

Circumcenter | The point of concurrency of the perpendicular bisectors of a triangle. |

Angle Bisector of a Triangle | A bisector of an angle of a triangle. |

Incenter | The point of concurrency of the angle bisectors of a triangle. |

Concurrency of Perpendicular Bisectors of a Triangle Theorem | The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle. |

Concurrency of Angle Bisectors of a Triangle Theorem | The angle bisectors of a triangle intersect at a point that is equidistant from the sides of a triangle. |

Median of a Triangle | A segment whose endpoints are a vertex of a triangle and the midpoint of the opposite side. |

Centroid | The point of concurrency of the three medians of a triangle. |

Altitude of a Triangle | The perpendicular segment from a vertex to the opposite side or to the line that contains the opposite side of a triangle. |

Orthocenter | The point of concurrency of the three altitudes of a triangle. |

Concurrency of Medians of a Triangle Theorem | The medians of are concurrent at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side. |

Concurrency of Altitudes of a Triangle | The lines containing the altitudes of a triangle are concurrent. |

Midsegment of a Triangle | A segment that connects the midpoints of two sides of a triangle. |

Midsegment Theorem | The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long. |

If one side of a triangle is longer than another side, the angle opposite the longer side is larger than the angle opposite the shortest side. | Theorem 5.10 |

If one angle of a triangle is lager than than another angle, then the side opposite the larger angle is longer than the side opposite the smallest angle. | Theorem 5.11 |

Exterior Angle Inequality Theorem | The measure of an exterior angle of a triangle is greater than the measure of either of the two nonadjacent interior angles. |

Triangle Inequality Theorem | The sum of the length of any two sides of a triangle is greater than the length of the third side. |

Polygon | A plane figure that meets the following conditions: 1. Formed by three or more segments called sides, such that no two sides with a common endpoint are collinear. 2. Each side intersects exactly two other sides, one at each endpoint(vertex). |

Quadrilateral | A 4 sided polygon |

Pentagon | A 5 sided polygon |

Hexagon | A 6 sided polygon |

Heptagon | A 7 sided polygon |

Octagon | An 8 sided polygon |

Nonagon | A 9 sided plygon |

Decagon | A 10 sided polygon |

Dodecagon | A 12 sided polygon |

n-gon | A n sided figure. |

Convex Polygon | A polygon in which no line that contains a side of the polygon contains a point in the interior of the polygon. |

Concave/Nonconvex Polygon | A polygon that is not convex. |

Regular Polygon | A polygon that is both equilateral and equiangular |

Diagonal of a Polygon | A segment that joins two nonconsecutive vertices of a polygon. |

Interior Angles of a Quadrilateral Theorem | The sum of the measures of the interior angles of a quadrilateral is 360 degrees. |

Polygon Interior Angles Theorem | The sum of the measures of the interior angels of a convex n-gon is (n-2)*180 |

Corollary to the Polygon Interior Angles Theorem | The measure of each interior angle of a regular n-gon is 1/n*(n-2)*180. |

Polygon Exterior Angles Theorem | The sum of the measures of the exterior angles of a convex, on angle at each vertex, is 360 degrees. |

Corollary to the Polygon Exterior Angles Theorem | The measure of each exterior angle of a regular n-gon is 360/n. |

Parallelogram | A quadrilateral with both pairs of opposite sides parallel. |

Opposite sides of a parallelogram are congruent | Theorem 6.2 |

Opposite angles of a parallelogram are congruent | Theorem 6.3 |

Consecutive angles of a parallelogram are supplementary | Theorem 6.4 |

The diagonals of a parallelogram bisect each other | Theorem 6.5 |

Proving Quadrilaterals are Parallelograms by Definition | If you can show that both pairs of opposite sides of a quadrilateral are parallel then it is a parallelogram |

If you can show that both pairs of opposite sides of a quadrilateral are congruent then it is a parallelogram | Theorem 6.6 |

If you can show that both pairs of opposite angles of a quadrilateral are congruent then it is a parallelogram | Theorem 6.7 |

If you can show that both pairs of consecutive angles in a quadrilateral are supplementary then it is a parallelogram | Theorem 6.8 |

If you can show that the diagonals of a quadrilateral are bisect each other then it is a parallelogram | Theorem 6.9 |

If you can show that one pair of opposite sides of a quadrilateral are both congruent and parallel then it is a parallelogram | Theorem 6.10 |

Rhombus | A parallelogram with 4 congruent sides. |

Rectangle | A parallelogram with 4 right angles. |

Square | A parallelogram with 4 right angles and 4 congruent sides. |

Special Parallelograms Memory Tip | A square is a rectangle and a rhombus, but a rectangle and a rhombus are never a square. Also when you combine a rectangle and a rhombus you get a square. |

A parallelogram is a rhombus if and only if its diagonals are perpendicular. | Theorem 6.11 |

A parallelogram is a rhombus if only if diagonal bisects a pair of opposite sides. | Theorem 6.12 |

A parallelogram is a rectangle if and only if its diagonals are congruent. | Theorem 6.13 |

Trapezoid | A quadrilateral with exactly one pair of parallel sides. |

Trapezoid Information | The parallel sides of a trapezoid are called the bases. The nonparallel sides are called legs. The angles that border the bases are called base angles. A trapezoid has two pairs of base angles. |

Isosceles Trapezoid | A trapezoid where the two legs are congruent. |

If a trapezoid is isosceles, then each pair of base angles are congruent. | Theorem 6.14 |

If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid. | Theorem 6.15 |

A trapezoid is isosceles if and only if its diagonals are congruent. | Theorem 6.16 |

Midsegment of a Trapezoid Theorem | The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases. |

Kite | A quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent. |

If a quadrilateral is a kite, then its bisectors are perpendicular. | Theorem 6.18 |

If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent. | Theorem 6.19 |

Circumscribe Circle | A circle with an inscribed polygon. |

Inscribed Polygon | A polygon whose verticies all lie on a circle. |

Created by:
monopoly10
on 2011-01-20

Copyright ©2001-2014 StudyStack LLC All rights reserved.