Chapter 5

Question 1

Perpendicular Bisector Theorem

Answer 1

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

Question 2

Converse of Perpendicular Bisector Theorem

Answer 2

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

Question 3

Concurrent Lines

Answer 3

3 or more lines that intersect at a common point

Question 4

Point of Concurrency

Answer 4

where concurrent lines intersect

Question 5

Circumcenter Theorem

Answer 5

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

Question 6

Angle Bisector Theorem

Answer 6

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

Question 7

Converse of Angle Bisector Theorem

Answer 7

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

Question 8

Incenter Theorem

Answer 8

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

Question 9

Median

Answer 9

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

Question 10

Centroid

Answer 10

• always on the interior of a triangle

- “balance point” of the triangle

Question 11

Centroid Theorem

Answer 11

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

Question 12

Altitude

Answer 12

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

Question 13

Orthocenter

Answer 13

Point where all of the altitudes are concurrent

Question 14

Perpendicular Bisectors

Answer 14

• must be a bisector
• must be perpendicular
• creates 2 congruent

Question 15

Comparison Property of Inequality

Answer 15

a<b>b</b>

Question 16

Transitive Property of Inequalities

Answer 16

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

Question 17

Addition Property of Inequality

Answer 17

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

if a <b></b>

Question 18

Subtraction Property of Inequality

Answer 18

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

if a<b></b>

Question 19

Exterior Angle Theorem

Answer 19

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

Question 20

Side- Angle Relationships

Answer 20

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.

Question 21

Angle-Side Relationships

Answer 21

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.

Question 22

Exterior Angle Inequality Theorem

Answer 22

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

Question 23

Triangle Inequality Theorem

Answer 23

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

Question 24

Hinge Theorem

Answer 24

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

Question 25

Converse of Hinge Theorem

Answer 25

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.