Chapter 5

Question 1

What is the midsegment of a triangle?

Answer 1

a segment connecting the midpoint of two sides

Question 2

Theorem 5-1 (midsegment theorem)

Answer 2

If a segment joins the midpoint of two sides of a triangle, then it is parallel to the third side and half it’s length

Question 3

Perpendicular bisector Theorem

Answer 3

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

Question 4

Converse of the Perpendicular Bisector Theorem

Answer 4

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

Question 5

Angle Bisector Theorem

Answer 5

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

Question 6

Converse of the Angle Bisector Theorem

Answer 6

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

Question 7

What does it mean if something is CONCURRENT?

Answer 7

3 or more lines intersect in one point

Question 8

What is the POINT OF CONCURRENCY?

Answer 8

The point in which concurrent lines intersect

Question 9

What are the four points of concurrency?

Answer 9

1. Circumcenter
2. Incenter
3. Centroid
4. Orthocenter

Question 10

What is a CIRCUMCENTER?

Answer 10

where perpendicular bisectors intersect

Question 11

What do you need to find to find the CIRCUMCENTER?

Answer 11

you must find the MIDPOINTS and PERPENDICULAR SLOPES

Question 12

Theorem 5-6

this theorem talks about circumcenters

Answer 12

The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices. The point of concurrency is called the circumcenter.

Question 13

What is an INCENTER?

Answer 13

where angle bisectors intersect

Question 14

Theorem 5-7

(this theorem is for incenters)

Answer 14

The bisector of the angles of a triangle are concurrent at a point equidistant from the sides. The point of concurrency is called the incenter of the triangle.

Question 15

What is a MEDIAN?

Answer 15

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

Question 16

What is a CENTROID?

Answer 16

where the medians intersect

Question 17

What do you need to find the CENTROID?

Answer 17

The midpoint and the vertices

Question 18

Theorem 5-8

theorem for centroid

Answer 18

The medians of a triangle are concurrent at a point that is 2/3 the distance from each vertex to the midpoint of the opposite side. The point of concurrency is called the centroid.

Question 19

What is an altitude?

Answer 19

the perpendicular segment from a vertex to the line containing the opposite side (height)

Question 20

What is an orthocenter?

Answer 20

where the altitudes intersect

Question 21

What do you need to find the orthocenter?

Answer 21

the perpendicular slope and the vertex

Question 22

Theorem 5-9

(this theorem is about the orthocenter)

Answer 22

The lines that contain the altitude of a triangle are concurrent. The point of concurrency is called the orthocenter of the triangle.

Question 23

Theorem 5-10 (sides)

Answer 23

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

Question 24

Theorem 5-11 (angles and sides)

Answer 24

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

in other words…the largest side is opposite the largest angle the middle angle is opposite the middle angle, and the shortest side is opposite the smallest angle

Question 25

Theorem 5-12 (side lengths sum)

Answer 25

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

OR

the sum of the 2 shortest sides must be greater than the third side

Question 26

formula for side lengths

Answer 26

v-w < side < v+w

y < x < z