Name:Mod 83

TERM

MEDIAN

ALTITUDE

Date:

Medians and Altitudes

DESCRIPTION

A segment from the —UZr-E<X— of a triangle

to the of the opposite side.

(segment from a

to the opposite side.

EX 1: Name each of the following:

Sides: b Ac BCMedian:

O Altitude: —Ab——

Period:

EXAMPLE

Draw and label median AD:

c

Draw and label altitude AD.

B c

c

Concurrencv of Medians of a Triangle - 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. This point is called the centroid and is the center

of balance of the triangle. arc

3 3

3

CD3 c

EX 2: Find the vålues of x and y given point Q is a centroid.

21

x12

C

Name: Date: Period:

Mod 8 3

EX 3: Find AB given AF is a median. 9

2x - 17

Practice Problem:1) Find the value of x and y given point P is a centroid.

24

18

c

2) Find BC given BF is a median.

BC =O

31 - 12

= 3 x-il

c

3) The vertices of a triangle are A(2,1), B (5, 8) and C(8, 3). Find the coordinates of the centroid.

Centroid=(

(3.stq.s)

Name:Mod 83

Date: Period:

Concurrency of Altitudes of a Triangle — The altitudes of a triangle intersect at a point called the

EX 4: Determine if the orthocenter falls inside, outside or on the triangle.

EX 5: Determine if the orthocenter falls inside, outside or on the triangle.

Oh 14

Based on your answers from the previous examples, where do you think the orthocenter would fall for an obtuse

triangle?

Practice Problem:3) Find the orthocenter of this triangle in coordinate

form.

o