Beyond CPCTC 3'4

1
Beyond CPCTC3.4
2
(No Transcript)
3
Vertices and Opposite side

• In triangle ABC side BC is opposite vertex A.
  Side AC is opposite vertex B.

B
A
C
4
Perpendicular Bisector

• Segment BD is a Perpendicular Bisector
• Segment BD bisects and is perpendicular to
  segment AC

5
Angle Bisector

• Segment BD bisects angle ADC.
• ltADB ? ltBDC

6
Median

• A segment whose endpoints are a vertex and the
  midpoint of the opposite side. Segment DB starts
  at vertex D and ends at point B, the midpoint of
  the opposite side AC.

7
Altitude

• A segment from a vertex that is perpendicular to
  the opposite side or to the line of the opposite
  side.

..\..\..\..\Geometry\Heath geometry\HChpt
5-Triangle Prop\03 Triangles\altitude area.gsp
8
Angle Bisector Converse

• Show and Tell
• ..\..\..\..\Geometry\Heath geometry\HChpt
  5-Triangle Prop\03 Triangles\Angle Bisectors.gsp

9
CentroidIntersection of Medians

• The intersection of the medians is called the
  centroid. The centroid is two-thirds of the
  distance from each vertex to the midpoint of the
  opposite side. A centroid is also the balance
  point for a triangle. Concurrent medians.

10
CentroidIntersection of Medians

• The intersection of the medians is called the
  centroid. The centroid is two-thirds of the
  distance from each vertex to the midpoint of the
  opposite side. A centroid is also the balance
  point for a triangle. Concurrent medians.

Draw the three medians.
11
CentroidIntersection of Medians

• The intersection of the medians is called the
  centroid. The centroid is two-thirds of the
  distance from each vertex to the midpoint of the
  opposite side. A centroid is also the balance
  point for a triangle. Concurrent medians.

B
F
C
O
D
Draw the three medians.
E
OD(1/3)CD
CO(2/3)CD
A
OF(1/3)AF
AO(2/3)AF
BO2OE
OE(1/2)BO
12
(No Transcript)