Geometry Terms

Front 1

statement

Back 1

states the theorem to be proved

Front 2

drawing

Back 2

represents the hypothesis of a theorem

Front 3

given

Back 3

describes the drawing according to the information found in the hypothesis of the theorem

Front 4

prove

Back 4

describes the drawing according to the claim made in the conclusion of the theorem

Front 5

proof

Back 5

orders a list of claims (statements) and justifications (reasons), beginning with the given and ending with the prove; there must be a logical flow in this proof

Front 6

statement vs. converse

Back 6

"all oranges are fruits" vs. "all fruits are oranges". Sometimes the converse of a statement is true (conjunction), and sometimes it isn't (disjunction).

Front 7

hypothesis

Back 7

statement of proof

Front 8

principle

Back 8

reason of proof

Front 9

conclusion

Back 9

next statement in proof

Front 10

point (postulate)

Back 10

a place on a line that has location but not size

Front 11

line

Back 11

infinite set of points

Front 12

collinear points

Back 12

two points on the same line

Front 13

line segment

Back 13

the portion of a line in between two distinct points

Front 14

congruent

Back 14

of the same length/degree

Front 15

bisecting

Back 15

separating into two parts of an equal measure

Front 16

perpendicular lines

Back 16

two lines that intersect and form congruent adjacent angles

Front 17

postulate

Back 17

assumed definition

Front 18

theorem

Back 18

a principle that can be followed logically

Front 19

isosceles triangle

Back 19

a triangle that has two congruent sides

Front 20

segment-addition postulate

Back 20

if X is a point of line AB and A-X-B, then AX + XB = AB

Front 21

midpoint

Back 21

the point of a line that separates the line segment into two equal parts

Front 22

parallel lines

Back 22

lines that lie on the same plane but do not intersect

Front 23

angle-addition postulate

Back 23

if a point D lies in the interior of of an angle ABC, then then the measure of angle ABD + the measure of angle DBC = the measure of angle ABC

Front 24

adjacent angles

Back 24

angles with a common side and vertex between them

Front 25

complementary angles

Back 25

two angles whose measure = 90 degrees

Front 26

supplementary angles

Back 26

two angles whose measure = 180 degrees

Front 27

vertical angles

Back 27

pairs of nonadjacent angles formed by intersecting straight lines

Front 28

addition property of equality

Back 28

if a = b, then a + c = b + c

Front 29

subtraction property of equality

Back 29

if a = b, then a - c = b - c

Front 30

multiplication property of equality

Back 30

if a = b, then a * c = b * c

Front 31

division property of equality

Back 31

if a = b and c is not 0, then a/c = b/c

Front 32

reflexive property

Back 32

a = a

Front 33

symmetric property

Back 33

if a = b, then b = a

Front 34

distributive property

Back 34

a(b + c) = a * b + a * c

Front 35

substitution property

Back 35

if a = b, then a replaces b in any equation

Front 36

transitive property

Back 36

if a = b and b = c, then a = c

Front 37

What is the first statement generally given in a proof?

Back 37

"given"

Front 38

What is the last statement generally given in a proof?

Back 38

"prove"

Front 39

What are the five parts of a formal theorem?

Back 39

1. State the theorem
2. Hypothesis
3. Given statement
4. Prove statement
5. Proof

Front 40

congruent complement/supplement theorem

Back 40

if two angles are complementary/supplementary to the same (congruent) angle, then those angles are congruent

Front 41

right angle theorem

Back 41

any two right angles will always be congruent

Front 42

orthogonal pairs

Back 42

two non-common sides of adjacent angles that form perpendicular rays

Front 43

ratio

Back 43

a quotient of two numbers

Front 44

proportion

Back 44

an equation stating that two or more ratios are equal

Front 45

similar polygons

Back 45

polygons that have all congruent corresponding angles and proportional corresponding sides

Front 46

similarity rule: AA~

Back 46

two angles of both triangles are congruent

Front 47

similarity rule: SSS~

Back 47

two corresponding sides of both triangles are proportional

Front 48

similarity rule: SAS~

Back 48

two angles and their forming sides are congruent and proportional

Front 49

side splitter theorem

Back 49

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

Front 50

triangle angle bisector theorem

Back 50

if a ray bisects an angle of a triangle, it divides the opposite side into segments that are proportional to the adjacent sides

Front 51

median of a triangle

Back 51

a line segment from the vertex to the midpoint of the opposite side

Front 52

altitude

Back 52

a line segment from a vertex to the line containing the opposite side

Front 53

common segment theorem

Back 53

if line AB is congruent to line CD, then line AC is congruent to line BC

Front 54

common angle theorem

Back 54

if angle AEB is congruent to angle CED, then angle AEC is congruent to angle BED

Front 55

What are the variables for a 30-60-90 triangle?

Back 55

a (shortest side), a√2 (medium side) 2a (hypotenuse)

Front 56

The ____est side is opposite the largest angle.

Back 56

longest

Front 57

What are the properties of a quadrilateral?

Back 57

1. diagonal separates it into two congruent angles
2. opposite angles are congruent
3. opposite sides are congruent
4. diagonals bisect each other
5. consecutive angles are supplementary

Front 58

altitude of a parallelogram

Back 58

a line segment from one vertex that is perpendicular to a nonadjacent side

Front 59

When is a quadrilateral a parallelogram?

Back 59

1. if two sides are both congruent and parallel
2. if both pairs of opposite sides are congruent

Front 60

kite

Back 60

a quadrilateral with two distinct pairs of congruent adjacent angles

Front 61

What are the properties of a rhombus?

Back 61

1. angle bisectors are perpendicular
2. four congruent sides
3. properties of a parallelogram

Front 62

What are the properties of a kite?

Back 62

1. one pair of opposite angles are congruent

Front 63

What are the properties of a rectangle?

Back 63

1. all right angles
2. diagonals are congruent
3. all properties of a parallelogram

Front 64

What are the properties of a trapezoid?

Back 64

1. base angles are congruent (isosceles)
2. diagonals are congruent (isosceles)
3. THE LENGTH OF THE MEDIAN OF A TRAPEZOID EQUALS ONE-HALF OF THE SUM OF THE TWO BASES
4. median is parallel to each base

Front 65

Explain a theorem involving three parallel lines and a transversal.

Back 65

if three (or more) parallel lines intercept congruent segments on one transversal, then they intercept congruent segments on any transversal