Name:
The
is the __________________ point of
the three __________________ of the triangle.
The orthocenter,
centroid, and
circumcenter
always lie in a
straight line, with
the ____________ in
the middle!
The
centroid is
always
___________
the
triangle.
How to find the centroid:
Find the midpoint of each
leg.
Draw a segment that
connects each midpoint to
the opposite vertex.
The
is also the ___________________ of ____________, or balancing point for the
triangle. Imagine cutting the triangle out and setting it on a pencil point. To keep it from tipping,
you would have to place the pencil tip directly under the centroid.
© Copyright 2015 Math Giraffe
B
A
The
is the __________________ point
of the __________________ (heights) of the 3 sides.
How to find the orthocenter:
Use your compass to measure the shortest side (𝐴𝐵). Using
that compass length with the point at vertex B, mark a small
arc at that length that intersects the opposite side (on 𝐴𝐶).
The
orthocenter
can be
inside or
outside of
the triangle.
C
Find the midpoint of segment that you marked off (from A to
the new point), and connect the midpoint to the original
vertex (B). Repeat using vertex A and its opposite side (𝐵𝐶).
The point that the two altitudes meet is the orthocenter. (You
can find the third, but only need two.)
Name:
The
The
incenter
is
always
____________
the
triangle.
is the __________________
When a triangle is
______________________,
all of the centers will be
at the same point!
point of the ___________________________
of the three vertices of the triangle.
How to find the
incenter:
Bisect each angle
and extend the
angle bisectors.
The
Find the point where
the three angle
bisectors meet.
is also the ___________________ of the
circle that could be __________________________ in the
triangle. Sketch this circle.
The
© Copyright 2015 Math Giraffe
is the __________________ point
of the _____________________________ of the 3 sides.
How to find the
circumcenter:
The
is
Construct a
perpendicular
bisector for each
side.
also the
___________________ of
the circle that this
Find the point
where the three
bisectors meet.
triangle could be
inscribed within. Sketch
this circle.
The
is __________________________ from all
three vertices. (This distance is the ____________ of the circle!)
The
circumcenter
can be inside
or outside of
the triangle.
Answer Key / Teacher Guide
Name:
intersection point of
is the __________________
The
medians
the three __________________
of the triangle.
The orthocenter,
centroid, and
circumcenter
always lie in a
straight line, with
centroid in
the ____________
the middle!
The
centroid is
always
inside
___________
the
triangle.
How to find the centroid:
Find the midpoint of each
leg.
Draw a segment that
connects each midpoint to
the opposite vertex.
center
mass or balancing point for the
is also the ___________________
of ____________,
The
triangle. Imagine cutting the triangle out and setting it on a pencil point. To keep it from tipping,
you would have to place the pencil tip directly under the centroid.
© Copyright 2015 Math Giraffe
B
The
intersection point
is the __________________
altitudes
of the __________________
(heights) of the 3 sides.
A
How to find the orthocenter:
Use your compass to measure the shortest side (𝐴𝐵). Using
that compass length with the point at vertex B, mark a small
arc at that length that intersects the opposite side (on 𝐴𝐶).
The
orthocenter
can be
inside or
outside of
the triangle.
C
Find the midpoint of segment that you marked off (from A to
the new point), and connect the midpoint to the original
vertex (B). Repeat using vertex A and its opposite side (𝐵𝐶).
The point that the two altitudes meet is the orthocenter. (You
can find the third, but only need two.)
Answer Key / Teacher Guide
Name:
The
The
incenter
is
always
____________
inside
the
triangle.
intersection
is the __________________
angle bisectors
point of the ___________________________
When a triangle is
______________________,
equilateral
all of the centers will be
at the same point!
of the three vertices of the triangle.
How to find the
incenter:
Bisect each angle
and extend the
angle bisectors.
The
Find the point where
the three angle
bisectors meet.
center
is also the ___________________
of the
inscribed
circle that could be __________________________
in the
triangle. Sketch this circle.
The
© Copyright 2015 Math Giraffe
intersection point
is the __________________
perpendicular bisectors of the 3 sides.
of the _____________________________
How to find the
circumcenter:
The
is
Construct a
perpendicular
bisector for each
side.
also the
center
___________________
of
the circle that this
Find the point
where the three
bisectors meet.
triangle could be
inscribed within. Sketch
this circle.
The
equidistant
is __________________________
from all
radius of the circle!)
three vertices. (This distance is the ____________
The
circumcenter
can be inside
or outside of
the triangle.