Chapter 5

Question 0

Perpendicular Bisector Theorem

Answer 0

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

Question 1

Perpendicular Bisector

Answer 1

A segment Bisector that is perpendicular to the segment it bisects.

Question 2

Perpendicular Bisector Converse Theorem

Answer 2

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

Question 3

Distance between a point and a line

Answer 3

Length of a perpendicular segment from the point to the line.

Question 4

Angle Bisector Theorem

Answer 4

If a point is on the Bisector of an angle, then it is equidistant from the two sides of the angle.

Question 5

Angle Bisector Converse Theorem

Answer 5

If a point is in the interior of an angle and is equidistant for the sides of the angle, then it lies in the Bisector of the angle.

Question 6

Perpendicular Bisector of a triangle

Answer 6

A segment that is part of a perpendicular Bisector of one of the sides

Question 7

Angle Bisector of a triangle

Answer 7

A segment that bisects one of the angles of the triangle.

Question 8

Median

Answer 8

A segment whose endpoints are a vertex and the midpoint I the opposite side (A median is always a segment Bisector, sometimes a perpendicular Bisector)

Question 9

Altitude

Answer 9

A segment from a vertex that is perpendicular to the opposite side or to the line containing the opposite side (An altitude may be inside or outside a triangle.)

Question 10

Notes #1

Answer 10

In an isosceles triangle, the perpendicular Bisector, angle Bisector, median, and altitude are all the same segment when the segment is drawn to the base.

Question 11

Notes #2

Answer 11

In an equilateral triangle, the perpendicular Bisector,angle Bisector, median, and altitude are all the same regardless of the sides the segment is drawn to.

Question 12

Concurrent Lines

Answer 12

A set of lines that share a single point of intersection

Question 13

Hinge Theorem

Answer 13

If two sides of one triangle are congruent to two sides of a second triangle, and the included angle of the first is greater than the included angle of the second, the the length of the third side of the first triangle is longer than the third side of the second triangle.

Question 14

Hinge Theorem Converse

Answer 14

If two sides of one triangle are congruent to two sides of a second triangle, and the third side of the first triangle is congruent to the third side of the second triangle, then the included angle of the first triangle is greater than the included angle of the second triangle.

Question 15

Midsegment

Answer 15

A segment that connects the midpoints of two sides of a triangle.

Question 16

Midsegment Theorem

Answer 16

In any triangle, a segment joining the midpoints of any two sides will be parallel to the third side and half its length.

Question 17

Triangle Inequality Theorem

Answer 17

Any side of a triangle is always shorter than the sum of the other two sides

Question 18

Circumcenter

Answer 18

The point of intersection of the three perpendicular bisectors of a triangle. (Equidistant from the vertices of a triangle)

Question 19

Incenter

Answer 19

The point of intersection of the three angle bisectors of a triangle. (Equidistant from the three sides of a triangle)

Question 20

Centroid

Answer 20

The point of intersection of the three medians of the triangle. (2/3 of the distance from each vertex to the midpoint of the opposite side.)

Question 21

Orthocenter

Answer 21

The point of intersection of the three altitudes of a triangle.