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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

slide2

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.

slide3

B

E

F

A

C

D

  • Name the 3 medians of triangle ABC.
  • BD
  • CF
  • AE
slide4

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)

slide5

AD & BE are altitudes of ABC.

AC & CD are altitudes of ABC.

BD & AE are altitudes of ABC

A

D

C

B

E

slide6

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.
slide9

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