Download 11-1B Inequalities in a Triangle - Winterrowd-math

11-1B Inequalities in a Triangle
What is orienteering?
What is the relationship
between an angle the opposite
side in a triangle?
Orienteering
• Orienteers can look at a map and
visualize their approach to every
checkpoint. Such maps are accurate
and detailed, and are prepared on a
human scale - terrain and features are
mapped so that what appears on the
map are the features that a human,
moving through the area, sees readily.
Orienteering skills applied
to Geometry
Like orienteering, if you look at an
accurate figure in Geometry, you
may be able to make a good guess
at which sides and angles are the
largest or smallest.
In Geometry, we must be able to
prove why.
The Littlest Angle
1.
2.
3.
4.
A
Draw a scalene triangle.
Measure the three sides.
Measure the three angles.
What relationship do you see
between the sides and the
angles?
C
B
Name the largest and smallest
angles
A
9
C
B
12
Name the largest and smallest
angles
D
5.6
110°
E
5.5
F
Name the largest and smallest
angles
S
4
R
5
5
3.9
Q
5
P
Name the longest and shortest
segments
A
30°
130°
B
20°
C
Name the longest and shortest
segments
T
65°
60° 75°
45°
50°
Q
65°
R
S
Name the longest and shortest
segments
V
49°
W
X
Theorems
If two sides of a triangle have unequal
lengths, then the measure of the angle
opposite the longer side is greater than
the measure of the angle opposite the
shorter side.
If two angles of a triangle have unequal
measures, then the side opposite the
large angle is longer than the side
opposite the smaller angle
• What is orienteering?
Orienteering uses a detailed map to
visualize their approach to every
checkpoint.
• What is the relationship between an
angle the opposite side in a triangle?
The largest angle is opposite the
longest side and the smallest angle is
opposite the shortest side.
Assignment 11-1B
• Page 717,
1-12, 27-38