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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 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

- 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

Concurrency of Medians of a Triangle Theorem

Substitute 8 for SQ.

So, QW 4 and SW 12.

- Practice

1. If BG 9, find BF.

2. If BD 12, find AD.

3. If CD 27, find GC.

- 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.

Can you answer these??????

- Look at the and answer the following
- 1. Is BD a median of ABC?
- 2. Is BD an altitude ABC?
- 3. Is BD a perpendicular bisector? B

B - A D C A D C

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