Chapter 5 Calendar
get a whiteboard!
1) Draw an acute triangle
• Draw all 3 angle bisectors
• Make all necessary markings
• Name their point of concurrency
• Show me
2) Draw an obtuse triangle
• Draw all 3 perpendicular bisectors
• Make all necessary markings
• Name their point of concurrency
• Show me
5-4: Altitudes and Medians
in Triangles
and
of Triangles
Median of a Triangle
·
𝑨
·
𝑴
₋
intersects a vertex and
the midpoint of a side
𝐶𝑀 is a median of ∆𝐴𝐵𝐶
𝑪
₋
is a
Median of
a Triangle
A line, segment, or ray
𝑩
Remember: Median is vertex to midpoint
Altitude of a Triangle
A line, segment, or ray
is an
Altitude of
a Triangle
intersects a vertex
and is ⊥ to the side
opposite that vertex
𝐶𝐷 is an alt. of ∆𝐴𝐵𝐶
𝑪
𝑨
·
⧠
𝑫
Remember: Altitude is vertex to ⊥
𝑩
Draw any triangle.
• Draw all 3 medians
(with correct markings!)
Draw an acute triangle.
• Draw all 3 altitudes
(with correct markings!)
Draw an obtuse triangle.
• Draw all 3 altitudes
(with correct markings!)
Concurrency of Medians Theorem
If
₌
₌
all 3 (or any 2)
medians
of a ∆ are drawn
·
·
· ·
then
they are concurrent
at a point that cuts
each median into
1/3 and 2/3
Centroid
·
Concurrency of Altitudes Theorem
If
all 3 (or any 2)
altitudes
of a ∆ are drawn
·
·
· ·
⧠
then
they are
concurrent at
a point
·
Orthocenter
𝑨
𝑨
𝑴
midsegment
₌
₌
𝑪
⊥ bisectors
𝑵
𝑩
·
·
·
· ·
·
·
· ·
·
·
· ·
₌
₌
⧠
∠ bisectors
medians
₌
₌
altitudes
⧠
𝑴𝑵 ∥ 𝑨𝑩 and
𝟏
𝑴𝑵 = 𝑨𝑩
𝟐
𝑴
𝑪
𝑩
·
·
· ·
·
𝑵
Circumcenter
⧠
Incenter
·
Centroid
·
Orthocenter
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