Chapter 5 Overview

Question 1

midsegments of a triangle

Answer 1

a segment connecting the midpoints of 2 sides of

the triangle

Question 2

Theorem 5-1 – Triangle Midsegment Theorem

Answer 2

If a segment joins the midpoints of 2 sides of a triangle, then the segment is
parallel to the third side and is half as long.

Question 3

equidistant

Answer 3

same distance from an object

Question 4

Theorem 5-2 Perpendicular Bisector Theorem

Answer 4

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

Question 5

Theorem 5-3 Converse of the Perpendicular Bisector Theorem

Answer 5

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

Question 6

distance from a point to a line

Answer 6

length of the ⊥ segment from the pt to the line

Question 7

Theorem 5-4 Angle Bisector Theorem

Answer 7

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

Question 8

Theorem 5-5 Converse of the Angle Bisector Theorem

Answer 8

If a pt in the interior of an angle is equidistant from the sides of the angle, then
the pt is on the angle bisector.

Question 9

concurrent

Answer 9

when 3 or more lines intersect at one pt

Question 10

point of concurrency

Answer 10

pt at which 3 or more lines intersect

Question 11

Theorem 5-6 – Concurrency of Perpendicular Bisectors Theorem

Answer 11

The ⊥ bisectors of the sides of a ∆ are concurrent at a pt equidistant from the
vertices.

Question 12

circumcenter of the triangle

Answer 12

pt of concurrency of the ⊥ bisectors of a ∆

Question 13

Theorem 5-7 – Concurrency of Angle Bisectors Theorem

Answer 13

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

Question 14

incenter of the triangle

Answer 14

pt of concurrency of the ∠ bisectors of a ∆

**always inside the triangle

Question 15

median of a triangle

Answer 15

a segment whose endpoints are a vertex and the

midpoint of the opposite side

Question 16

Theorem 5-8 – Concurrency of Medians Theorem

Answer 16

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

Question 17

centroid of the triangle

Answer 17

the pt of concurrency of the medians

**always inside the ∆

Question 18

altitude of a triangle

Answer 18

the perpendicular segment from the vertex of a ∆ to the
line containing the opposite side

• it can be inside or outside of the ∆ or it can be a side of the ∆

Question 19

Theorem 5-9 – Concurrency of Altitudes Theorem

Answer 19

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

Question 20

orthocenter of the triangle

Answer 20

pt of concurrency of the altitudes of a ∆

Question 21

indirect reasoning

Answer 21

all possibilities are considered and then all but one are

proved false

Question 22

indirect proof

Answer 22

a proof involving indirect reasoning

Step 1 – State as a temporary assumption the opposite (negation) of what you want to prove.

Step 2 – Show that this temporary assumption leads to a contradiction.

Step 3 – Conclude that the temporary assumption must be false and that what you want to prove must be true.

Question 23

Comparison Property of Inequality

Answer 23

If a = b + c and c > 0, then a > b.

Question 24

Corrolary to the Triangle Exterior Angle Theorem

Answer 24

The measure of an exterior ∠ of a ∆ is greater than the measure of each of its
remote interior angles.

Question 25

Theorem 5-10

Answer 25

If 2 sides of a ∆ are not congruent, then the larger angle lies opposite the longer
side.

Question 26

Theorem 5-11

Answer 26

If 2 angles of a ∆ are not congruent, then the longer side lies opposite the larger
angle.

Question 27

Theorem 5-12 Triangle Inequality Theorem

Answer 27

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

Question 28

Theorem 5-13 – The Hinge Theorem (SAS Inequality Theorem)

Answer 28

If 2 sides of one ∆ are ≅ to two sides of another ∆, and the included angles are
not ≅, then the longer third side is opposite the larger included angle.

Question 29

Theorem 5-14 – Converse of the Hinge Theorem (SSS Inequality)

Answer 29

If 2 sides of one ∆ are ≅ to two sides of another ∆, and the 3rd sides are not ≅,
then the larger included angle is opposite the longer 3rd side.