Chapter 5

Question 1

Perpendicular Bisector Theorem

Answer 1

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

Question 2

Converse of Perp. Bisector Theorem

Answer 2

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

Question 3

Perpendicular Bisector

Answer 3

a line that is perpendicular to a segment at it’s midpoint

Question 4

Angle Bisector Theorem

Answer 4

If a point is on the bisector of an angle, then it is equidistant from the 2 sides of the angle

Question 5

Converse of Angle Bisector Theorem

Answer 5

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 the angle

Question 6

Circumcenter of a Triangle

Answer 6

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

Question 7

Concurrency of Perp. Bisectors of Triangle

Answer 7

The perp. bisector of a triangle intersect at a point that is equidistant from the vertices

Question 8

Concurrency of Angle Bisectors of a Triangle

Answer 8

The angle bisectors of a triangle intersect at a point that is equidistant from the sides

Question 9

Incenter of a Triangle

Answer 9

The point of concurrency of the angle bisectors

Question 10

Median of a Triangle

Answer 10

Line that connects a vertex and the midpoint of the opposite side

Question 11

Centroid of a Triangle

Answer 11

Point of concurrency of the midpoints

Question 12

Altitude of a Triangle

Answer 12

Perpendicular segment from a vertex to the opposite side or the line that connects opposite side

Question 13

Orthocenter of a Triangle

Answer 13

Point of concurrency of the altitudes

Question 14

Concurrency of Medians of a Triangle

Answer 14

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

Question 15

Concurrency of Altitudes of a Triangle

Answer 15

The lines containing the altitudes of a triangle are congruent

Question 16

Midsegment

Answer 16

the segment connecting the midpoints of 2 sides of a triangle is parallel to the 3rd side and is half as long

Question 17

Theorem 5.10`

Answer 17

If 1 side of a triangle is longer than the other side, then the angle opposite the longer side is larger than the angle opposite the shorter side

Question 18

5.11

Answer 18

If 1 angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle

Question 19

Exterior Angle Inequality Theorem

Answer 19

The measure of an exterior angle of a triangle is greater than the measure of either of the 2 nonadjacent interior angles

Question 20

Triangle Inequality Theorem

Answer 20

The sum of the lengths of any 2 sides of a triangle is greater than the length of the 3rd side

Question 21

Hinge Theorem

Answer 21

If 2 sides of 1 triangle are congruent to 2 sides of another triangle, and the included angle of the 1st triangle is larger than the included angle of the 2nd triangle, then the 3rd side of the 1st triangle is longer than the 3rd side of the 2nd triangle

Question 22

Converse to the Hinge Theorem

Answer 22

If 2 sides of 1 triangle are congruent to 2 sides of another congruent triangle, and the 3rd side of the 1st triangle is longer than the 3rd side of the 2nd triangle then the included of the 1st triangle is larger than the angle of the 2ne triangle