Chapter 5 Flashcards Preview

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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

ab

16

Transitive Property of Inequalities

if ab 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

Converse of Hinge Theorem

If 2 sides of a triangle are congruent to 2 sides of another triangle, and the 3rd side in the first triangle is larger than the 3rd side in the second, then the included angle measure of the first triangle is greater than the included angle measure in the 2nd triangle.