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Beyond CPCTC

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# Beyond CPCTC - PowerPoint PPT Presentation

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

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:

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)

AD & BE are altitudes of ABC.

AC & CD are altitudes of ABC.

BD & AE are altitudes of ABC

A

D

C

B

E

Could an altitude also be a median?

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

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.

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