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Beyond CPCTC

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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. – PowerPoint PPT presentation

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Title: Beyond CPCTC


1
Beyond CPCTC
  • Lesson 3.4

2
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.
3
B
E
F
A
C
D
  • Name the 3 medians of triangle ABC.
  • BD
  • CF
  • AE

4
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)
5
AD BE are altitudes of ABC.
AC CD are altitudes of ABC.
BD AE are altitudes of ABC
A
D
C
B
E
6
Could an altitude also be a median? Yes, for an
isosceles triangle when drawn from the vertex.
7
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 its length.

8
Postulate Two points determine a line, ray or
segment.
Determine (one and only one line)
9
  1. Given
  2. An altitude of a forms rt. ?s with the side to
    which it is drawn.
  3. Same as 2
  4. If ?s are rt. ?s, they are ?.
  5. Reflexive Property.
  6. Given
  7. ASA (4, 5, 6)
  8. CPCTC
  9. Subtraction Property (6 from 8)
  1. CD BE are altitudes of ABC.
  2. ?ADC is a rt. ?.
  3. ?AEB is a rt. ?.
  4. ?ADC ? ?AEB
  5. ?A ? ?A
  6. AD ? AE
  7. ADC ? AEB
  8. AB ? AC
  9. DB ? EC
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