Beyond CPCTC

1
Section 3.4

• Beyond CPCTC

2
Median
A
median

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

C
B
3
Median
A
median

• A median divides the opposite side into two
  congruent segments, or bisects the side to which
  it is drawn.

C
B
4
Median
A

• Every triangle has three medians.

C
B
5
Altitude
altitude

• An altitude of a triangle is a line segment drawn
  from any vertex of the triangle to the opposite
  side, extended if

A
C
B

• necessary, and perpendicular to that side.

6
Altitude
altitude

• An altitude of a triangle forms a right angle
  with the side to which it is drawn.

A
C
B
7
Altitude

• Every triangle has three altitudes.

A
C
B
8
Median or Altitude?

• Identify the median(s) and altitude(s) shown in
  each of the following diagrams

Median(s) Altitude(s)
9
Median or Altitude?

• Identify the median(s) and altitude(s) shown in
  each of the following diagrams

Median(s) Altitude(s)
10
Postulate

• Two points determine a line (or ray or segment).

11
Auxiliary Lines

• Given
• Prove

12
Auxiliary Lines

• Sometimes, it may be necessary or helpful to add
  lines, rays, or segments to a given diagram. We
  can connect any two points already in our
  diagram, using the previous postulate as
  justification any two points determine a line.

13

• Given
• Prove

Statements
Reasons
Given
1.
1.
Two points determine a line.
2.
2.
Reflexive Property
3.
3.
SSS (1, 1, 3)
4.
4.
CPCTC
5.
5.