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