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 TrianglesGEOMETRY

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

X

Y

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

X

Y

Z

Let’s Practice• Write the sides of the following triangles in order from longest to

shortest:

X

Y

Z

57⁰ 64⁰

Let’s Practice• Write the sides of the following triangles in order from longest to

shortest:

X

Y

Z

60⁰36⁰

Let’s Practice• Write the angles of the following triangle in order from largest to

smallest:

X

Y

Z10 cm

5.5 cm 8 cm

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

X

Y

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