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Beyond CPCTC. Lesson 3.4. Medians : Every triangle has 3 medians A median is a line segment drawn from any vertex to the midpoint of its opposite side. A median bisects the segment. B. E. F. A. C. D. Name the 3 medians of triangle ABC. BD CF AE. Altitudes :

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Beyond cpctc

Beyond CPCTC

Lesson 3.4


Beyond cpctc

Medians: Every triangle has 3 medians

A median is a line segment drawn from any vertex to the midpoint of its opposite side.

A median bisects the segment.


Beyond cpctc

B

E

F

A

C

D

  • Name the 3 medians of triangle ABC.

  • BD

  • CF

  • AE


Beyond cpctc

Altitudes:

Every triangle has 3 altitudes.

An altitude is a line segment drawn perpendicular from any vertex to its opposite side.

*The altitude could be drawn outside the triangle to be perpendicular.

Altitudes form right angles 90˚

You may need to use auxiliary lines (lines added)


Beyond cpctc

AD & BE are altitudes of ABC.

AC & CD are altitudes of ABC.

BD & AE are altitudes of ABC

A

D

C

B

E


Beyond cpctc

Could an altitude also be a median?

Yes, for an isosceles triangle when drawn from the vertex.


Midsegments
MidSegments

  • A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle.

  • The midsegment is parallel to the third side and is half it’s length.


Beyond cpctc

Postulate: Two points determine a line, ray or segment.

Determine (one and only one line)


Beyond cpctc

  • Given

  • An altitude of a forms rt. s with the side to which it is drawn.

  • Same as #2

  • If s are rt. s, they are .

  • Reflexive Property.

  • Given

  • ASA (4, 5, 6)

  • CPCTC

  • Subtraction Property (6 from 8)

  • CD & BE are altitudes of ABC.

  • ADC is a rt. .

  • AEB is a rt. .

  • ADC  AEB

  • A  A

  • AD  AE

  • ADC  AEB

  • AB  AC

  • DB  EC