Geometry Ch 5 - Relationships Within Triangles

Question 1

Midsegment of a Triangle

Answer 1

A segment connecting the midpoints of two sides.

Question 2

Triangle Midsegment Theorem

Answer 2

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

Question 3

Midpoint Formula

Answer 3

Question 4

Distance Formula

Answer 4

Question 5

Perpendicular Bisector Theorem

Answer 5

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

Question 6

Converse of the Perpendicular Bisector Theorem

Answer 6

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

Question 7

Distance from a Point to a Line

Answer 7

The length of the perpendicular segment from the point to the line.

Question 8

Angle Bisector Theorem

Answer 8

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

Question 9

Converse of the Angle Bisector Theorem

Answer 9

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

Question 10

Concurrent Lines

Answer 10

When three or more lines intersect in one point.

Question 11

Point of Concurrency

Answer 11

The point at which concurrent lines intersect.

Question 12

The perpendicular bisectors of the sides of a triangle…

Answer 12

…are congruent at a point equidistant from the vertices.

Question 13

The bisectors of the angles of a triangle…

Answer 13

are concurrent at a point equidistant from the sides.

Question 14

Circumcenter of the Triangle.

Answer 14

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

Question 15

Circumscribed (about)

Answer 15

To draw (a figure) around another, touching it at points but not cutting it.

Question 16

Incenter of the Triangle

Answer 16

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

Question 17

Inscribed (in)

Answer 17

To draw (a figure) within another so that their boundaries touch but do not intersect.

Question 18

Median of a Triangle

Answer 18

A segment whose endpoints are a vertex and the midpoint of the opposite side.

Question 19

The medians of a triangle are concurrent at…

Answer 19

… a point that is two thirds the distance from each vertex to the midpoint of the opposite side.

Question 20

Centroid of a Triangle

Answer 20

In a triangle, the point of concurrency of the median. The point is also called the Center of Gravity of a triangle because it is the point where a triangular shape will balance.

Question 21

Center of Balance of a Triangle

Answer 21

The centroid, because it is the point where a triangular shape will balance.

Question 22

Altitude of a Triangle

Answer 22

The perpendicular segment from a vertex to the line containing the opposite side. Unlike angle bisectors and medians it can be a side of a triangle or it may lie outside the triangle.

Question 23

Orthocenter of a Triangle

Answer 23

The point at which the lines containing the altitudes of a triangle are concurrent.

Question 24

The lines that contain the altitudes of a triangle…

Answer 24

… are concurrent.

Question 25

Negation of a Statement

Answer 25

Has the opposite truth value.

Question 26

Inverse of a Conditional Statement

Answer 26

Negates both the hypothesis and the conclusion. A conditional and its inverse can (but may not) have different truth values.

Question 27

Contrapositive of a Conditional Statement

Answer 27

Switches the hypothesis and the conclusion and negates both. It ALWAYS has the same truth value as the conditional. Thus, a conditional statement and its contrapositive are equivalent.

Question 28

Equivalent Statements

Answer 28

Have the same truth value.

Question 29

Comparison Property of Inequality

Answer 29

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

Question 30

Corollary to the Triangle Exterior Angle Theorem

Answer 30

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

Question 31

If two sides of a triangle are not congruent…

Answer 31

… then the larger angle lies opposite the longer side.

Question 32

If two angles of a triangle are not congruent…

Answer 32

…then the longer side lies opposite the larger angle. This is converse of Theorem 5-10.

Question 33

Triangle Inequality Theorem

Answer 33

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