Download December 21

Geometry
December 21, 2016
5.6 Triangle Inequalities
DO NOW
Hint: median segment lengths are in
the ratio 1 : 2 : 3
Agenda
• Announcements (2nd hour only)
• Do Now
• Review: Medians and Altitudes
• Practice
• Inequalities in a Triangle
I can identify and apply
triangle midsegments,
medians, and altitudes.
Median
Point of
concurrency:
Centroid
(Center of
gravity)
Median
The centroid cuts
each median into
two segments. The
longer segment is
twice the length of
the shorter one.
Altitude
The altitude of a
triangle is
perpendicular to
one side and goes
through the
opposite vertex.
Altitude
Altitudes can intersect inside, on, or outside
the triangle.
Exercises
Triangle Inequalities
1. An exterior angle is always larger than
either remote interior angle.
Triangle Inequalities
2. Larger angles are always opposite larger
sides (and vice versa).
Triangle Inequalities
3. The lengths of the two shorter sides of a
triangle are more than the length of the
longest side.
Exercises
List the angles of each triangle from smallest
to largest.
Exercises
List the lengths of each side from shortest to
longest.
Exercises
Can a triangle have the given side lengths?
Exercises
Given two side lengths, what is the shortest
and longest the third side could be?
1. 8 ft, 12 ft
2. 5 in, 16 in
3. 6 cm, 6 cm