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 ˚
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 it’s length.

8. Postulate: Two points determine a line, ray or segment.
Determine (one and only one line)

9. 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.
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