Sketch obtuse triangle ABC with B obtuse' a' Sketch altitude BD' b' Sketch median BE'

1
Sketch obtuse triangle ABC with? B obtuse.
a. Sketch altitude BD. b. Sketch median BE.
B
C
A
D
E
2
Think for a moment about an angle bisector...
A
B
C
3
Is BD an angle bisector?
A
D
30
60
B
C
4
Is BE an angle bisector?
A
E
44
46
B
C
5
Is BF an angle bisector?
A
F
45
45
B
C
6
Constructing Angle Bisectors

• Objectives
• 1. Discover method for constructing an angle
  bisector.
• 2. Look at how to construct special angles by
  combining 60 and 90 angles.

7
angle bisector - ray that has an endpoint on the
vertex of the angle and that divides the angle
into two angles of equal measure
8

• C-4 - Angle Bisector ConjectureIf a point
  is on the angle bisector of an angle, then it is
  __________ from the sides of the angle.

equidistant
9
1. With your compass set on the vertex of your
angle, draw an arc that crosses both rays of
your angle.
10
2. The arc intersects each ray of the angle.
From each intersection point, draw another arc so
your arcs intersect.
11
3. Draw a ray from the vertex of your angle
through the arc intersection point. This is the
angle bisector.
12
Measure each anglethey should be congruent!
13
Draw obtuse angle BIG.

• Construct the angle bisector.

B
I
G
14

• Think about the first step used to construct an
  angle bisector..

15

• What is the next step in constructing an angle
  bisector?

16

• What is the last step?

17
Constructing Equilateral Triangles

• 1. Sketch a segment.

18

• 1. Sketch a segment.

19

• 2. Measure length of segment with compass.

20

• 3. From each endpoint, construct a circle
  using the measurement from 2.

21

22

• 2. Make two segments from endpoints of segment
  to arc intersection point.

23

24

• You have an equilateral triangle!!!

25

• Measure each angle of your triangle..

26

• C-5 The measure of each angle of an equilateral
  triangle is ___

60
27
Practice Compass and straightedge construct an
equilateral triangle.
28
What is the measure of each angle of this
triangle?
60
29
How could we compass and straightedge construct a
30 angle?
30

• Closure

1. Is ray RY an angle bisector? Why?
Y
YES
48.5
48.5
R
31
2. When constructing an angle bisector, the
first arc to be made is here. True or False.
TRUE