Chapter 5

Question 1

Midsegment Theorem

Answer 1

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

Question 2

Perpendicular Bisector Theorem

Answer 2

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

Question 3

Converse of the Perpendicular Bisector Theorem

Answer 3

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

Question 4

Concurrency of Perpendicular Bisectors
Theorem

Answer 4

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

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.

Question 6

Converse of the Angle Bisector Theorem

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 the 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 the triangle

Question 8

Concurrency of Medians of a Triangle

Answer 8

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

Question 9

Concurrency of Altitudes of a Triangle

Answer 9

The
lines containing the altitudes of a triangle are
concurrent.

Question 10

What happens if one side of a triangle is longer then the other?

Answer 10

If one side of a triangle is longer than another
side, then the angle opposite the longer side
is larger than the angle opposite the shorter
side.

Question 11

What happens if one angle is larger is the other?

Answer 11

If one 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 12

Triangle Inequality Theorem

Answer 12

The sum of
the lengths of any two sides of a triangle is
greater than the length of the third side

Question 13

Hinge Theorem

Answer 13

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

Question 14

Converse of the Hinge Theorem

Answer 14

f two sides
of one triangle are congruent to two sides of
another triangle, and the third side of the first
is longer than the third side of the second,
then the included angle of the first is larger
than the included angle of the second

Question 15

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Answer 15

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