GeometryGeometry

Today:Today:• 5.5 Instruction5.5 Instruction• PracticePractice

Only the Only the educated are educated are free.free.

EpictetusEpictetus

5.5 5.5 Inequalities in One TriangleInequalities in One Triangle

ObjectivesObjectives::1.1. Compare measurements in Compare measurements in

triangles triangles

VocabularyVocabulary::nonenone

5.5

CCSSCCSS

Content Standards

G.CO.10 Prove theorems about triangles.

G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy

physical constraints or minimize cost; working with typographic grid systems based on ratios).

Mathematical Practices

1 Make sense of problems and persevere in solving them.

2 Reason abstractly and quantitatively.

Then/NowThen/Now

You recognized and applied properties of inequalities to the relationships between the angles

and sides of a triangle.

• Use the Triangle Inequality Theorem to identify possible triangles.

• Prove triangle relationships using the Triangle Inequality Theorem.

5.5 Inequalities in One Triangle5.5 Inequalities in One Triangle

Name three sets of Name three sets of lengths that make lengths that DO NOT a successful triangle. make a triangle. _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____

5.5 Inequalities in One Triangle5.5 Inequalities in One 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.

A

CB

AC + BC > AB

5.5

Can the given side lengths form a triangle?

a.) 6, 7, 15

b.) 6,13, 9

c.) 6, 8, 14

5.5

7x

Given the triangle below, find a range of values to represent x.

5.5

9

If a triangle has sides of 15 m and 27 m, what is the range of values for the third side of the triangle?

5.5

5.5 Inequalities in One Triangle5.5 Inequalities in One Triangle

What is the largest angle of the given triangle?

B

CA

5.5

5 7

3

5.5 Inequalities in One Triangle5.5 Inequalities in One Triangle

Theorem:

If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.

5.5

List the angles from least to greatest.

5.5

FE

D

Find the value of x.

110

46

5.5

X + 103X - 5

Over Lesson 5–3

A. A and D

B. B and F

C. C and E

D. A and B

KITE ASSEMBLY Tanya is following directions for making a kite. She has two congruent triangular pieces of fabric that need to be sewn together along their longest side. The directions say to begin sewing the two pieces of fabric together at their smallest angles. At which two angles should she begin sewing?

A triangle is formed by three kitchen appliances as shown in the figure.

The distances shown are measured in feet. What is wrong with the labels?

5.5

50°

60°

70°

10

6

8

refrigerator

sink

range

GeometryGeometry

Assignment:Assignment:• 5.5 p366 #1-5, 22, 5.5 p366 #1-5, 22,

25-31 odd25-31 odd

Only the Only the educated are educated are free.free.

EpictetusEpictetus