Chapter Five

Question 1

Concurrency of perpendicular bisectors of a triangle

Answer 1

The perpendicular bisectors of a triangle intersect at a point that is equidistant from the verticies of the triangle

Question 2

Converse of the perpendicular bisectors theorem

Answer 2

In a plane If a point is equidistant from the end points of a segment, then it is on the perpendicular bisector

Question 3

Perpendicular bisector theorem

Answer 3

In a plane if a point is on the perpendicular bisector of a segment the it is equidistant from the end points of the segment

Question 4

Mid segment theorem

Answer 4

The segments connecting the midpoints of the two sides of a triangle is parallel to the third side and is half as long as that side

Question 5

Angle bisector theorem

Answer 5

If a point is on the bisector of an angle then it is equidistant from the two sides of the angle (the ones at 90)

Question 6

Converse of the angle bisector

Answer 6

If a point is in the interior of an angle and is equidistant from the sides of the angle then it lies on the bisector of an angle

Question 7

Concurrency of angle bisectors of a triangle

Answer 7

The angle bisectors of a triangle intersect at a point that is equidistant from the sides of a triangle
(Three lines with the 90 degrees)

Question 8

Concurrency of medians of a triangle

Answer 8

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

Question 9

Concurrency of altitudes of a triangle

Answer 9

The lines connecting the altitudes of a triangle are concurrent

Question 10

Altitude

Answer 10

A perpendicular line segment connecting a side to its opposite vertex

Question 11

Centroid

Answer 11

The point where all three medians intersect

Question 12

Circumcenter

Answer 12

The point where all perpendicular bisectors intersect

Question 13

Incenter

Answer 13

The point where all angle bisectors intersect

Question 14

Median

Answer 14

A segment from a vertex to the midpoint of the opposite side

Question 15

Orthocenter

Answer 15

The point where all three altitudes intersect

Question 16

Perpendicular bisector

Answer 16

A line that is perpendicular to a segment at its midpoint

Question 17

Point of concurrency

Answer 17

The point where lines intersect

Question 18

Vertex

Answer 18

A point that joins two sides of a triangle

Question 19

Bisect

Answer 19

To divide into two congruent parts

Question 20

Angle bisector

Answer 20

A day that divides an angle into two angles that are congruent

Question 21

Is the circumcenter equidistant from all vertices

Answer 21

Yes

Question 22

Does a perpendicular bisector cuts through the midpoint of a segment

Answer 22

Yes

Question 23

Does a median cut through the midpoint of a segment

Answer 23

Yes

Question 24

Is a point on an angle bisector equidistant from two sides of the triangle

Answer 24

Yes

Question 25

Is t possible for a median altitude perpendicular bisector and an angle bisector to be all represented by the same line in a triangle

Answer 25

Yes

Question 26

Can any point of concurrency ever meet outside a triangle

Answer 26

No

Question 27

Is the centroid 2/3 distance from the vertex of the median

Answer 27

Yes

Question 28

Can altitudes from a vertex meet the opposite side at an angle other than 90

Answer 28

No

Question 29

Concurrency

Answer 29

Three or more lines that meet at a point