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Geometry > Chapter 5-6 > Flashcards

Chapter 5-6 Flashcards

0
Q

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

A

perpendicular bisector theorem

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1
Q

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

A

perpendicular bisector

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2
Q

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

A

converse of the perpendicular bisector theorem

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3
Q

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

A

concurrent lines

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4
Q

the point where concurrent lined intersect

A

point of concurrency

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5
Q

the point of concurrenc of the perpendicular bisectors

A

circumcenter

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6
Q

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

A

circumcenter theorem

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7
Q

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

A

angle bisector theorem

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8
Q

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

A

converse of the angle bisector theorem

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9
Q

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

A

incenter

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10
Q

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

A

median

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11
Q

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

A

centroid

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12
Q

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

A

centroid theorem

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13
Q

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

A

altitude

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14
Q

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

A

orthocenter

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15
Q

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

A

definition of inequality

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16
Q

ab

A

comparison property of inequality

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17
Q
  1. if a<b>b and b>c, then a>c</b>
A

transitive property of inequality

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18
Q
  1. if a>b, then a+c>b+c

2. if a<b+c

A

addition property of inequality

19
Q
  1. if a>b, then a-c>b-c

2. if a<b-c

A

subtraction property of inequality

20
Q

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

A

exterior angle inequality

21
Q

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

A

angle-side relationships in triangles

22
Q

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

A

indirect reasoning

23
Q

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

A

indirect proof or proof by contradiction

24
Q

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

A

triangle inequality theorem

25
Q

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

A

hinge theorem

26
Q

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

A

converse of the hinge theorem

27
Q

a segment tht connects any two nonconsecutive vertices

A

diagonal

28
Q

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

A

polygon interior angles sum

29
Q

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

A

polygon exterior angles sum

30
Q

a quadrilateral with both pairs of opposite sides parallel

A

parallelogram

31
Q
  • 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
A

diagonals of parallelograms

32
Q

a parallelogram with four right angles

A

rectangle

33
Q

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

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

A

diagonals of a rectangle

34
Q

a parallelogram with all four sides congruent

A

rhombus

35
Q

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

A

diagonals of a rhombus

36
Q

a parallelogram with four congruent sides and four right angles

A

square

37
Q

a quadrilateral with exactly one pair of parallel sides

A

trapezoid

38
Q

the parallel sides of a trapezoid

A

bases

39
Q

the nonparallel sides in a trapezoid

A

legs

40
Q

angles formed by the base and one of the legs

A

base angles

41
Q

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

A

isosceles trapezoid

42
Q
  • 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
A

isosceles trapezoid

43
Q

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

A

mid-segment of a trapezoid

44
Q

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

A

trapezoid mid-segment theorem

45
Q

a quadrilateral with exactly two pairs of consecutive congruent sides

A

kite

46
Q
  • 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
A

kites

Geometry (7 decks)

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