# Definitions, Postulates, Theorems for chapters 1-7 for Geometry

### 154 terms by lilaznboi3214

#### Study  only

Flashcards Flashcards

Scatter Scatter

Scatter Scatter

## Create a new folder

u can't really test urself on this........ its just kinda like familiarizing urself with the stuff

Ruler Postulate

### on line AB in a given plane, choose any point O between A and B. Consider ray OA and ray OB and all the rays that can be drawn from O on one side of line AB. These rays can be paired with the real numbers from 0 to 180 in such a way that: ray OA is paired with 0, and ray OB with 180, or, if ray OP is paired with X, and ray OQ with y, then angle POQ = l x-y l.

Protractor Postulate

Postulate 5

Postulate 6

postulate 7

Postulate 8

Postulate 9

Theorem 1-1

Theorem 1-2

Theorem 1-3

Midpoint Theorem

### If ray BX is the bisector of angle ABC, then angle ABX = 1/2angleABC and angle XBC = 1/2 angle ABC

Angle Bisector Theorem

### Reasons used in Proofs

Given info, Definitions, Postulates (and properties from algebra), Proven Theorems

Theorem 2-3

### Complementary angles

two angles whose measures have the sum 90

### Supplementary angles

two angles whose measures have the sum 180

Theorem 2-4

Theorem 2-5

Theorem 2-6

Theorem 2-7

Theorem 2-8

### Parallel lines

coplanar lines that do not intersect

### Skew lines

noncoplanar lines

Theorem 3-1

### two nonadjacent interior angles on opposite sides of the transversal

Alternate interior angles

### Same-Side Interior Angles

two interior angles on the same side of the transversal

### two angles in corresponding positions relative to the two lines

Corresponding angles

Postulate 10

Theorem 3-2

Theorem 3-3

Theorem 3-4

Postulate 11

Theorem 3-5

Theorem 3-6

Theorem 3-7

Theorem 3-8

Theorem 3-9

Theorem 3-10

### Ways to prove two lines parallel

show that a pair of corresponding angles are congruent

### Ways to prove two lines parallel

show that a pair of alternate interior angles are congruent

### Ways to prove two lines parallel

show that a pair of same-side interior angles are supplementary

### Ways to prove two lines parallel

in a plane show that both lines are perpendicular to a third line

### Ways to prove two lines parallel

show that both lines are parallel to a third line

### Triangle

figure formed by three segments joining three noncollinear points

### Scalene Triangle

no sides congruent

### Isosceles Triangle

at least two sides congruent

### Equilateral triangle

all sides congruent

### Acute triangle

three acute angles

one obtuse angle

one right angle

### Equiangular triangle

all angles congruent

Theorem 3-11

Corollary 3-1

Corollary 3-2

Corollary 3-3

Corollary 3-4

Theorem 3-12

many angles

### Convex Polygon

polygon such that no line containing a side of the polygon contains a point in the interior of the polygon

Theorem 3-13

Theorem 3-14

### Inductive Reasoning

reasoning that is widely used in science and everyday life

### Deductive Reasoning

conclusion based on accepted statements (definitions, postulates, previous theorems, corollaries, and given information) conclusion MUST be true if hypotheses are true

### Inductive Reasoning

Conclusion based on several past observations. conclusion is PROBABLY true, but not necessarily true

### Congruent

having the same size and shape

### SSS postulate

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

### SAS postulate

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

### ASA postulate

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

### A way to prove two segments or two angles are congruent

identify two triangles in which the two segments or angles are corresponding parts

### A way to prove two segments or two angles are congruent

prove that the triangles are congruent

### A way to prove two segments or two angles are congruent

state that the two parts are congruent, using the reason CPCTC

### Isosceles Triangle Theorem

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

Corollary 4-1

Corollary 4-2

Corollary 4-3

Theorem 4-2

Corollary 4-4

### AAS theorem

if two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, then the triangls are congruent

### HL theorem

if the hypotenuse and a leg of one right triangle

### Ways to prove triangles congruent

SSS, SAS, ASA, AAS

HL

### Median

segment from a vertex to the midpoint of the opposite side in a triangle

### Altitude

perpendicular segment from a vertex to the line that contains the opposite side in a triangle

### Perpendicular bisector

line (or ray or segment) that is perpendicular to the segment at its midpoint

Theorem 4-5

Theorem 4-6

Theorem 4-7

Theorem 4-8

Theorem 5-1

Theorem 5-2

Theorem 5-3

Theorem 5-4

Theorem 5-5

Theorem 5-6

Theorem 5-7

### Ways to prove that a quadrilateral is a parallelogram

show that BOTH pairs of opposite sides are parallel

### Ways to prove that a quadrilateral is a parallelogram

show that BOTH pairs of opposite sides are congruent

### Ways to prove that a quadrilateral is a parallelogram

show that ONE pair of opposite sides are both congruent and parallel

### Ways to prove that a quadrilateral is a parallelogram

show that both pairs of opposite angles are congruent

### Ways to prove that a quadrilateral is a parallelogram

show that the diagonals bisect each other

Theorem 5-8

Theorem 5-9

Theorem 5-10

Theorem 5-11

### Rectangle

quadrilateral with four right angles

### Rhombus

quadrilateral with four congruent sides

### Square

quadrilateral with four right angles and four congruent sides

Theorem 5-12

Theorem 5-13

Theorem 5-14

Theorem 5-15

Theorem 5-16

Theorem 5-17

Theorem 5-18

Theorem 5-19

### Exterior Angle Inequality Theorem

the measure of an exterior angle of a triangle is greater than the measure of either remote interior angle

Inverse

Contrapositive

Given statement

Converse

### How to write an Indirect Proof

Assume temporarily that the conclusion is not true

### How to write an Indirect Proof

reason logically until you reach a contradiction of a known fact

### How to write an Indirect Proof

point out that the temporary assumption must be false, and that the conclusion must then be true

Theorem 6-2

Theorem 6-3

Corollary 6-1

Corollary 6-2

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

Triangle Inequality

### SAS Inequality Theorem

if two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first trangle is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle

### SSS Inequality Theorem

if two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second, then the included angle of the first triangle is larger than the included angle of the second

### Ratio

quotient when the first number is divided by the second

### Property of Proportions

a/b = c/d is equivalent to ad = bc

### Property of Proportions

a/b = c/d is equivalent to a/c = b/d

### Property of Proportions

a/b = c/d is equivalent to b/a = d/c

### Property of Proportions

a/b = c/d is equivalent to a+b/b = c+d/d

### Property of Proportions

if a/b = c/d = e/f =..., then a + c +e +.../b + d + f + ... = a/b = ...

### AA ~

if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar

### SAS Similarity Theorem

if an angle of one triangle is congruent to an angle of another triangle and the sides including those angles are in proportion, then the triangles are similar

### SSS Similarity Theorem

if the sides of two triangles are in proportion, then the triangles are similar

### Triangle Proportionality Theorem

if a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally

### Triangle Angle-Bisector Theorem

if a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the other two sides

space

collinear points

coplanar points

intersection

### two lines that intersect to form right angles

Perpendicular lines

See More

Example:

## Press Ctrl-0 to reset your zoom

### Please upgrade Flash or install Chrometo use Voice Recording.

For more help, see our troubleshooting page.

Create Set