Download REVIEW OF SOME BASIC IDEAS

Entry Task
• In Webgeogebra.org construct a triangle.
• Carefully measure each side and angle in each triangle.
• List the sides of the triangle in order from longest to shortest.
• List the angles of each triangle from largest to smallest.
• What do you notice about the relationship between the longest
side and the largest angle? What about the shortest side and the
smallest angle? If you drag a vertex around, does it change this
releationship?
Section 5-5 Inequalities
in Triangles
GEOMETRY
11/06/15
Theorem
• If two sides of a triangle are not congruent, then the larger angle
lies opposite the longer side (and the smaller angle lies opposite
the shorter side).
• EX: if XZ > XY, then m∡Y > m∡Z
Y
X
Z
Theorem – Conversely…
• If two angles of a triangle are not congruent, then the longer side
lies opposite the larger angle (and the shorter side lies opposite
the smaller angle).
• EX: if m∡Y > m∡Z, then XZ > XY
Y
X
Z
Let’s Practice
• Write the sides of the following triangles in order from longest to
shortest:
Y
X
57⁰
64⁰
Z
Let’s Practice
• Write the sides of the following triangles in order from longest to
shortest:
Y
X
60⁰
36⁰
Z
Let’s Practice
• Write the angles of the following triangle in order from largest to
smallest:
Y
X
10 cm
Z
Sides of a Triangle
• Can a triangle be formed from any three side
lengths?
• Write your answer in your notebook
Spaghetti Triangles
• Break one piece of spaghetti into three pieces
and create a triangle.
Spaghetti Triangles
• Did it work?
• If it did not, use your second piece of
spaghetti to create a side lengths that will
work.
• If it did work, use your second piece of
spaghetti to create side lengths that do not
work.
Spaghetti Triangles
• What do you notice about the relationship
between the side lengths for the triangle that
did work, versus the triangle that did not
work?
• Within your group try to make a conjecture
about the relationship between the side
lengths of a triangle.
Triangle Inequality Theorem
• The sum of the lengths of any two sides of a triangle is greater
than the length of the third side.
• XY + YZ > XZ
• XZ+XY > YZ
• YZ + XZ > YX
Y
X
Z
Let’s Practice
• Write whether the following could be possible sides of a triangle:
• 3 ft, 7 ft, 8 ft
• 3 in, 10 in, 6 in
• 7cm, 12cm, 19cm
Let’s Practice
• A triangle has side lengths of 8 cm and 10 cm. What are the
possible side lengths for the 3rd side?
• Write the answer on your white board.
Homework
Pg 328; problems 1-4, 9, 16, 28, 30, 37