Flashcards in Chapter 5 Deck (25):

1

## Perpendicular Bisector Theorem

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

2

## Converse of Perpendicular Bisector Theorem

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

3

## Concurrent Lines

### 3 or more lines that intersect at a common point

4

## Point of Concurrency

### where concurrent lines intersect

5

## Circumcenter Theorem

### The perpendicular bisectors of the sides of a triangle are concurrent at a point called the circumcenter that is equidistant from the vertices of a triangle

6

## Angle Bisector Theorem

### If a point is on the bisector of an angle, then it is equidistant from the sides of the angle

7

## Converse of Angle Bisector Theorem

### If a point in the interior of an angle is equidistant from the sides of an angle, then it is on the angle's bisector

8

## Incenter Theorem

### The angle bisectors of a triangle are concurrent at a point called the incenter. The incenter is equidistant from the sides of the triangle

9

## Median

### -endpoints are a vertex of the triangle and midpoint of the opposite side

10

## Centroid

###
-always on the interior of a triangle

-"balance point" of the triangle

11

## Centroid Theorem

### The medians of a triangle intersect at a point called the centroid that is two-thirds of the distance from each midpoint of the opposite side

12

## Altitude

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

13

## Orthocenter

### Point where all of the altitudes are concurrent

14

## Perpendicular Bisectors

###
-must be a bisector

-must be perpendicular

-creates 2 congruent

15

## Comparison Property of Inequality

###
a**b**

16

## Transitive Property of Inequalities

###
if a**b and b>c, then a>c**

17

## Addition Property of Inequality

###
if a>b, then a+b>b+c

if a

18

## Subtraction Property of Inequality

###
if a>b, then a-c>b-c

if a

19

## Exterior Angle Theorem

### The measure of an exterior angle of a triangle is greater than either of it's corresponding remote interior angles

20

## Side- Angle Relationships

### If one side of a triangle is larger than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side.

21

##
Angle-Side Relationships

### If one angle of a triangle is greater in measure than another angle in the triangle, then the side opposite the bigger angle is longer than the side opposite the smaller angle.

22

## Exterior Angle Inequality Theorem

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

23

## Triangle Inequality Theorem

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

24

## Hinge Theorem

### If two sides of a triangle are congruent to two sides of another triangle, and the included angle of the first triangle is larger than the included angle of the 2nd triangle, than the 3rd side of the first triangle is larger than the third side of the second triangle

25