Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
54 Cards in this Set
- Front
- Back
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. |
|
Linear Pair Perpendicular Theorem |
If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. |
|
Perpendicular Transversal Theorem |
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other. |
|
Lines Perpendicular to a Parallel Transversal theorem |
In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. |
|
Transitive Property of Parallel lines |
If two lines are parallel to the same third line, then they are parallel to each other. |
|
Corresponding Angles Theorem |
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. |
|
Alternate Exterior Angles Theorem |
If the two lines are parallel, then the theorem tells you that thealternate exterior angles are congruent to each other. |
|
Corresponding Angles Converse |
If two lines are cut by a transversal so that the corresponding angles are congruent, then the lines are parallel.
|
|
Alternate Exterior Angles Converse |
If two lines are cut by a transversal so that the alternate exterior angles are congruent, then lines are parallel. |
|
Alternate Interior Angles Theorem |
If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. |
|
Alternate Interior Angles Converse |
If two lines are cut by a transversal so that the alternate exterior angles are congruent, then the lines are parallel. |
|
Consecutive Interior Angles Converse |
If two lines are cut by a transversal so that the consecutive interior angles are supplementary, then the lines are parallel. |
|
Segment Addition Postulate |
If B is between A and C, then AB+BC=AC |
|
Angle Addition Postulate |
If a ray lies in the interior of an angle, then the sum of the measures of the two smaller angles is equal to the larger angle. |
|
Two-point Postulate |
Through any two points there is exactly one line. |
|
Line-point Postulate |
A line contains at least two points. |
|
Three-point Postulate |
Through any three non co-linear points there exists exactly one plane. |
|
Plane-point Postulate |
A plane contains at least three non co-linear |
|
Line-Intersect Postulate |
If two lines intersect, then their intersection is exactly one point. |
|
Plane- line Postulate |
If two points lie in a plane, then the line containing them lies in the plane. |
|
Plane-Intersect Postulate |
If two planes intersect, then their intersection is exactly one line. |
|
Definition of a midpoint |
A midpoint separates a segment into two congruent segments. |
|
Definition of an Angle Bisector |
An angle bisector divides an angle into two congruent angles. |
|
Addition Property of Equality |
If you add the same number to both sides of an equation, then the equation remains true. |
|
Subtraction Property of |
If you subtract the same number from both sides of an equation, then the equation remains true. |
|
Multiplication/Division Property of Equality |
If you multiply of divide the same number on each side of an equation, then the equation remains true. |
|
Substitution Property of Equality |
If x = y, then x can be substituted in for y in any equation, and y can be substituted for x in any equation. |
|
Transitive Property of Equality or Congruence |
If a=b and b=c, then a=c. |
|
Definition of a right angle |
A right angle equals 90 degrees. |
|
Definition of Congruence |
Congruent geometric segments have equal measures. |
|
Definition of Perpendicular |
Perpendicular lines intersect to create two right angles. |
|
Definition of Complementary Angles |
If the sum of two angles is equal to 90 degrees, then they are complementary. |
|
Definition of Supplementary Angles |
If the sum of two angles are 180 degrees, then the angles are supplementary. |
|
Linear Pair Postulate |
If two angles form a linear pair, than they are supplementary. |
|
Right Angles are Congruent |
If two angles are right angles, then they are congruent. |
|
Vertical Angles are Congruent |
If two angles are vertical angles, then they are congruent. |
|
Supplements of Congruent Angles |
If <1 & <2 are supp, and <4 & <2 are supp, then <1 & <4 are congruent. |
|
Complements of Congruent Angles |
If <1 & <2 are comp, and <4 & <2 are comp, then <1 &<4 are congruent. |
|
Corresponding Angles Theorem |
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. |
|
Corresponding Angle Converse Postulate |
If two lines are cut by a transversal so that a pair of corresponding angles are congruent, then the lines are parallel. |
|
Alternate Interior Angles Converse Theorem |
If two lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the lines are parallel. |
|
Alternate Exterior Angles Converse Theorem |
If two lines are cut by a transversal to that a pair of alternate exterior angles are congruent, then the lines are parallel. |
|
Consecutive Interior Angles Converse Theorem |
If two lines are cut by a transversal so that a pair of consecutive interior angles are congruent, then the lines are parallel. |
|
Base Angles Theorem |
If two sides of a triangle are congruent, then the angles opposite them are congruent. |
|
Converse of the Base Angles Theorem |
If two angles of a triangle are congruent, then the sides opposite them are congruent. |
|
Corollary to 5.2 |
If a triangle is equilateral, then it is also equiangular. |
|
Corollary to 5.3 |
If a triangle is equiangular, then it is also equilateral. |
|
Side-Angles-Side Congruence Theorem |
If two sides and the included angles of one triangle are congruent and two sides and the included angle of another triangle, then the two triangles are congruent. |
|
Side-Side-Side Congruence Theorem |
If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. |
|
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 triangle, then the two triangles are congruent. |