Chapter 5-6

Question 0

if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment

Answer 0

perpendicular bisector theorem

Question 1

if a bisector is also perpendicular to the segment it is called this

Answer 1

perpendicular bisector

Question 2

if a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment

Answer 2

converse of the perpendicular bisector theorem

Question 3

when three or more lines intersect at a common point, the lines are called this

Answer 3

concurrent lines

Question 4

the point where concurrent lined intersect

Answer 4

point of concurrency

Question 5

the point of concurrenc of the perpendicular bisectors

Answer 5

circumcenter

Question 6

the perpendicular bisectors of a triangle intersect at a point called the circumcenter that is equidistant from the vertices of the triangle

Answer 6

circumcenter theorem

Question 7

if a point on the bisector of an angle, then it is equidistant from the sis of the angle

Answer 7

angle bisector theorem

Question 8

if a point n the interior of an angle is equidistant from the sides of the angle, then it is on h bisector of the angle

Answer 8

converse of the angle bisector theorem

Question 9

the angle bisectors of a triangle are concurrent, and their point of concurrency is called this

Answer 9

incenter

Question 10

a segment with endpoints being a vertex of a triangle and the midpoint of the opposite side

Answer 10

median

Question 11

the point of concurrency of the medians of a triangle and is always inside the triangle

Answer 11

centroid

Question 12

the medians of triangle intersect at a point called this that is 2/3 of the distance from each vertex to the midpoint of the opposite side

Answer 12

centroid theorem

Question 13

a segment from a vertex to the line containing the opposite side and perpendicular to the line containing that side

Answer 13

altitude

Question 14

the lines containing the altitude of a triangle are concurrent, intersecting at a point called this

Answer 14

orthocenter

Question 15

for an real numbers a and b, a>b if and only if there is a positive number c such that a=b+c

Answer 15

definition of inequality

Question 16

ab

Answer 16

comparison property of inequality

Question 17

1. if a<b>b and b>c, then a>c</b>

Answer 17

transitive property of inequality

Question 18

1. if a>b, then a+c>b+c

2. if a<b+c

Answer 18

addition property of inequality

Question 19

1. if a>b, then a-c>b-c

2. if a<b-c

Answer 19

subtraction property of inequality

Question 20

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

Answer 20

exterior angle inequality

Question 21

if one side of a triangle is longer than another side, the the angle opposite the longer side has a greater measure than the angle opposite the shorter side
-same with angles of a triangle

Answer 21

angle-side relationships in triangles

Question 22

assuming that a conclusion was false and then showing that this assumption led to a contradiction

Answer 22

indirect reasoning

Question 23

a proof in which you temporarily assume that what you are trying to prove is false

Answer 23

indirect proof or proof by contradiction

Question 24

the sum of the lengths of any two sides of a triangle must be greater than the length of the third side

Answer 24

triangle inequality theorem

Question 25

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

Answer 25

hinge theorem

Question 26

if two sides of a triangle are congruent to two sides of another triangle, and the third side in the first is longer than the second triangle, then the included angle measure of the first triangle is greater than the included angle measure in the second triangle

Answer 26

converse of the hinge theorem

Question 27

a segment tht connects any two nonconsecutive vertices

Answer 27

diagonal

Question 28

the sum of the interior angle measures of an n-sided convex polygon is (n-2)*180

Answer 28

polygon interior angles sum

Question 29

the sum of the exterior angle measures of a convex polygon, one angle at each vertex, is 360

Answer 29

polygon exterior angles sum

Question 30

a quadrilateral with both pairs of opposite sides parallel

Answer 30

parallelogram

Question 31

- if a quadrilateral is a parallelogram, then its diagonals bisect each other - if a quadrilateral is a parallelogram, then each diagonal separates the parallelogram into two congruent triangles

Answer 31

diagonals of parallelograms

Question 32

a parallelogram with four right angles

Answer 32

rectangle

Question 33

if a parallelogram is a rectangle, then its diagonals are congruent if diagonals of a parallelogram are congruent, then the parallelogram is a rectangle

Answer 33

diagonals of a rectangle

Question 34

a parallelogram with all four sides congruent

Answer 34

rhombus

Question 35

if a parallelogram is a rhombus, then its diagonals are perpendicular if a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles

Answer 35

diagonals of a rhombus

Question 36

a parallelogram with four congruent sides and four right angles

Answer 36

square

Question 37

a quadrilateral with exactly one pair of parallel sides

Answer 37

trapezoid

Question 38

the parallel sides of a trapezoid

Answer 38

bases

Question 39

the nonparallel sides in a trapezoid

Answer 39

legs

Question 40

angles formed by the base and one of the legs

Answer 40

base angles

Question 41

if the legs of a trapezoid are congruent, then it is this

Answer 41

isosceles trapezoid

Question 42

- if a trapezoid is isosceles, then each pair of base angles is congruent - if a trapezoid has one pair of congruent base angles then it is an isosceles trapezoid - a trapezoid is isosceles if and only if its diagonals are congruent

Answer 42

isosceles trapezoid

Question 43

the segment that connects the midpoints of the legs of the trapezoid

Answer 43

mid-segment of a trapezoid

Question 44

the mid-segment of a trapezoid is parallel to each base and its measure is one half the sum of the lengths of the bases

Answer 44

trapezoid mid-segment theorem

Question 45

a quadrilateral with exactly two pairs of consecutive congruent sides

Answer 45

kite

Question 46

- if a quadrilateral is a kite, then its diagonals are perpendicular - if a quadrilateral is a kite then exactly one pair of opposite angles is congruent

Answer 46

kites