Geometry 5

Question 1

circumcenter

Answer 1

intersection of the perpendiular bisectors of the sides of a triangle

Question 2

incenter

Answer 2

intersection of the angle bisectors of the vertices of the triangle

Question 3

concurrent lines?

Answer 3

3 or more lines intersecting at one point

Question 4

Is the incenter ever outside of the triangle?

Answer 4

No

Question 5

When can the circumcenter be outside the triangle?

Answer 5

if the triangle is obtuse

Question 6

When can the circumcenter of the triangle be on a side

Answer 6

if the triangle is right

Question 7

When can the circumcent be inside the triangle?

Answer 7

when it is acute

Question 8

What is the circumcenter always equidistant to?

Answer 8

the vertices

Question 9

What is the incenter always equidistant to?

Answer 9

the sides

Question 10

when is the incenter equidistant to the vertices/ or the circumcenter equidistant to the sides

Answer 10

if the triangle is equilateral.

Question 11

incircle versus circumcircle

Answer 11

the circle made from the intersections of the lines perpendicular to the sides is the incircle-
The circle made from the vertices of a triangle is the circumcircle.

Question 12

5.1&5.2 Perpendicular bisector theorem&converse

Answer 12

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

Question 13

5.5&5.4 Angle bisector theorem&converse.

Answer 13

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

Question 14

Circumcenter theorem

Answer 14

The circumcenter of a triangle is equidistant from the vertices

Question 15

Incenter theorem

Answer 15

The incenter of a triangle is equidistant from it’s sides.

Question 16

medians

Answer 16

lines in a triangle from a vertax to the mid point of the opposite side.

Question 17

altitudes

Answer 17

A line showing the distance of a vertex from the opposite line, altitude is perpendicular to opposite line.

Question 18

Centroid

Answer 18

Intersection of the medians! ALWAYS inside triangle.

-2/3s the distance from the vertex t the opposite side (2/3s the way on the median)

Question 19

Orthocenter

Answer 19

intersection of all the altitudes.

Question 20

What do
-Altitudes
-Medians
- perpendicular bisectors
- angle bisectors
intersect to form?

Answer 20

• altitudes- orthocenter
• medians- centroid (center of gravity)
• perpendicular bisectors- circumcenter
• angle bisector- incenter

Question 21

What is the definition of inequalities

Answer 21

5=2+3
THEN
5 is greater than 2 and 3

Question 22

Theorem 5.8(Exterior angle inequality)

Answer 22

because m^1+m^2=m^3
THEN
m^1<m^3
and
m^2<m^3

Question 23

Theorem 5.9&5.10
-ASA relationships

Answer 23

• AB>BC so m^B> m^A
• CONVERSE

Question 24

comparison (properties of real numbers)

Answer 24

a<b, a=b, OR a>b

Question 25

5.11 Triangle inequality theorem

Answer 25

sides a,b and c
a+b<c
b+c<a
c+a<b

Question 26

what is an indirect proof