Chapter 5 sections 1, 2, &3 vocabulary

Question 1

Midsegment

Answer 1

A segment connecting the midpoints of two sides.

Question 2

Coordinate Proof

Answer 2

Using geometry and algebra to prove the Triangle Midsegment Theorem. (choose variables for the coordinates of the verticies)

Question 3

Distance From a Point to a Line

Answer 3

The length of a perpendicular segment from a point to a line.

Question 4

Concurrent

Answer 4

When 3 or more lines intersect in one point

Question 5

Point of Concurrency

Answer 5

The point where concurrent lines intersect.

Question 6

Circumcenter of Triangle

Answer 6

The point of concurrency of the perpendicular bisectors of a triangle.

Question 7

Circumscribed about

Answer 7

When a circle is surrounding a triangle.

Question 8

Incenter of the triangle

Answer 8

The point of concurrency of the angle bisectors of a triangle.

Question 9

Inscribed in

Answer 9

When the circle is inside the triangle

Question 10

Median of a triangle

Answer 10

a segment whose endpoints are a vertex and the midpoint of the opposite side.

Question 11

Centroid

Answer 11

The point of concurrency of the medians

Question 12

Orthocenter of the triangle

Answer 12

The point where the lines containing the altitudes of a triangle are concurrent.

Question 13

Theorem 5-1

Answer 13

Triangle Midsegment Theorem:
- If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side, and is half its length.

Question 14

Theorem 5-2

Answer 14

Perpendicular Bisector Theorem:

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

Question 15

Theorem 5-3

Answer 15

Converse of the Perpendicular Bisector Theorem:

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

Question 16

Theorem 5-4

Answer 16

Angle Bisector Theorem:

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

Question 17

Theorem 5-5

Answer 17

Converse of the Angle Bisector Theorem:
- If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector.

Question 18

Theorem 5-6

Answer 18

The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices.

Question 19

Theorem 5-7

Answer 19

The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides.

Question 20

Theorem 5-8

Answer 20

The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite side.

Question 21

Theorem 5-9

Answer 21

The lines that contain the altitudes of a triangle are concurrent.