Chapter 5

Question 0

Coordinate Proof

Answer 0

When proving the triangle Midsegment Theorem use coordinate geometry and algebra

Question 1

Triangle Midsegment Theorem

Answer 1

if a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and half its length

Question 2

Theorem 5-2 Perpendicular Bisector Theorem

Answer 2

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

Question 3

Theorem 5-3 Converse of Perpendicular Bisector Theorem

Answer 3

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

Question 4

Theorem 5-4 Angle Bisector Theorem

Answer 4

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

Question 5

Theorem 5-5 Converse of Angle Bisector Theorem

Answer 5

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

Question 6

Distant from a point to a line

Answer 6

The distance from a point to a line is the length o the perpendicular segment from the point to a line

Question 7

Theorem 5-6

Answer 7

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

Question 8

Theorem 5-7

Answer 8

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

Question 9

Concurrent

Answer 9

When three or more lines intersect in one point

Question 10

Point of concurreny

Answer 10

The point at with they intersect is the point of concurrency

Question 11

Circumcenter of the triangle

Answer 11

The point at which they intersect is the circumcenter of the triangle

Question 12

Theorem 5-8

Answer 12

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

Question 13

Centroid

Answer 13

The point of concurrency of medians is the centroid

Question 14

Median of a triangle

Answer 14

A median of a triangle is a segments whose endpoints are a vertex and the midpoint of the opposite side

Question 15

Altitude

Answer 15

An altitude of a triangle is the perpendicular segment from a vertex to the line containing the opposite side

Question 16

Negation

Answer 16

The negation of a statement has the opposite truth value

Question 17

Inverse

Answer 17

The inverse of a conditional statement negates both the hypothesis and the conclusion

Question 18

Contrapositive

Answer 18

The contrapositive of a conditional switches both the hypothesis and the conclusion and negates both

Question 19

Equivalent statements

Answer 19

Statements that have the same truth value

Question 20

Indirect reasoning

Answer 20

All possibilities are considered until all but one are proved false. The remaining possibility must be true

Question 21

Indirect proof

Answer 21

A proof involving indirect reasoning is called an indirect proof. In such a proof, a statement and its negation often are the only possibilities

Question 22

Comparison property of inequality

Answer 22

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

Question 23

Corollary to the triangle angle sum theorem

Answer 23

The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles

Question 24

Theorem 5-10

Answer 24

If two sides of a triangle are not congruent, then the larger angle lies opposite the larger side

Question 25

Theorem 5-11

Answer 25

If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle

Question 26

Theorem 5-12 Triangle Inequality Theorem

Answer 26

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