# 5.4 Medians and Altitudes - PowerPoint PPT Presentation

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## 5.4 Medians and Altitudes

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### 5.4 Medians and Altitudes Vocabulary Concurrent- 3 or more lines, rays, or segments that intersect at the same point Median of a Triangle a segment from a ... – PowerPoint PPT presentation

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Title: 5.4 Medians and Altitudes

1
5.4 Medians and Altitudes
2
Vocabulary
• Concurrent- 3 or more lines, rays, or segments
that intersect at the same point
• Median of a Triangle a segment from a vertex to
the midpoint of the opposite side
• Centroid point of concurrency of 3 medians
• Altitude of a Triangle the perpendicular
segment from a vertex to the opposite side or to
the line that contains the opposite side there
are 3 in a

3
• Orthocenter - the point where the 3 altitudes of
a intersect
• Theorem 5.8 Concurrency of Medians
• of a
• -the medians of a intersect at a point
that is 2/3 the distance from each vertex to the
midpoint of the opposite side.
• Theorem 5.9 Concurrency of Altitudes
• of a
• -the lines containing the altitudes of a
• are concurrent

4
Concurrency of Medians of a Triangle Theorem
Substitute 8 for SQ.
So, QW 4 and SW 12.
5
• Practice

1. If BG 9, find BF.
2. If BD 12, find AD.
3. If CD 27, find GC.
6
• Find the orthocenter.

Find the orthocenter P in an acute, a right, and
an obtuse triangle. (Draw 3 altitudesdrop
perpendicular lines from vertex to opposite side.)
SOLUTION
Acute triangle P is inside triangle.
Right triangle P is on triangle.
Obtuse triangle P is outside triangle.
7