Lecture 5.3 & 5.5 - Triangle Inequalities

​5.3 - Inequalities in One Triangle

Get ready to EAT again​

​states that an exterior angle is greater than either of its corresponding remote angles​

​Exterior Angle Inequality Theorem

​

Multiple Choice

Use the Exterior Angle Inequality Theorem to list all angles that satisfy the stated condition: measures are less than  $$\angle1$$   ​

• $$\angle3,\ \angle4,\ \angle5,\ \angle7,\ \angle8$$  

• $$\angle3,\ \angle4,\ \angle5,\ \angle6,\ \angle8$$  

• $$\angle2,\ \angle6,\ \angle7,\ \angle8$$  

• $$\angle2,\ \angle6,\ \angle8,\ \angle9$$  

Multiple Choice

Use the Exterior Angle Inequality Theorem to list all angles that satisfy the stated condition: measures are less than  $$\angle3$$   ​

• $$\angle2,\ \angle6,\ \angle8,\ \angle9$$  

• $$\angle1,\ \angle6,\ \angle8$$  

• $$\angle5,\ \angle7,\ \angle8$$  

• $$\angle2,\ \angle4,\ \angle7,\ \angle8$$  

Multiple Choice

Use the Exterior Angle Inequality Theorem to list all angles that satisfy the stated condition: measures are greater than  $$\angle2$$   ​

• $$\angle1,\ \angle6,\ \angle8,\ \angle9$$  

• $$\angle1,\ \angle6,\ \angle8$$  

• $$\angle6,\ \angle9$$  

• $$\angle3,\ \angle5,\ \angle6,\ \angle8,\ \angle9$$  

Reorder

Use the Exterior Angle Inequality Theorem to list the following angles from least to greatest​

•  7

•  5

•  3

•  1

1

2

3

4

• 1
• 2
• 3
• 4

Multiple Select

Use the Exterior Angle Inequality Theorem to select all angles that satisfy the stated condition: measures are less than  $$\angle9$$    ​

•   $$\angle8$$  

•   $$\angle6$$  

•   $$\angle1$$  

•   $$\angle3$$  

• $$\angle2$$  

Multiple Select

Use the Exterior Angle Inequality Theorem to select all angles that satisfy the stated condition: measures are less than  $$\angle4$$     ​

•   $$\angle8$$  

•   $$\angle6$$  

•   $$\angle1$$  

•   $$\angle3$$  

• $$\angle2$$  

Multiple Select

Use the Exterior Angle Inequality Theorem to select all angles that satisfy the stated condition: measures are greater than  $$\angle7$$     ​

•   $$\angle9$$  

•   $$\angle5$$  

•   $$\angle1$$  

•   $$\angle3$$  

• $$\angle2$$  

​states that by knowing either the side lengths or angle measures, the unkown opposite angles or sides can be ordered in ascending or descending order

​

​Angle-Side

Relationships in

Triangles

Multiple Choice

What is the smallest angle?

• J
• K
• L

Multiple Choice

What is the largest angle?

• K
• L
• M

Multiple Choice

• VW

• WU

• UV

• None

Multiple Choice

• RQ

• QS

• SR

• None

Multiple Choice

• A

• B

• C

• D

Multiple Choice

• QR

• PQ

• PR

• SR

Multiple Choice

Order the sides of the triangle from least to greatest.

• B, C, A
• AC, CB, BA
• BA, AC, CB
• CB, AB, AC

​5.5 - The Triangle Inequality Theorem

Will it triangle?

​states that the sum of any two sides of a triangle must be greater than the length of the third side

​Triangle Inequality Theorem

Multiple Select

Which of the following sets of side lengths could produce a triangle. SELECT ALL THAT APPLY.

• 4, 4, 4

• 5, 5, 10

• 3, 6, 9

• 5, 7, 11

• 13, 5, 6

Multiple Choice

Will these side lengths form a triangle?

• yes

• no

Multiple Choice

Will these side lengths form a triangle?

• yes

• no

Multiple Choice

Will these line segments form a triangle?

• yes

• no

Multiple Choice

Will these three sides form a triangle?

• yes

• no

Multiple Choice

Which of these lengths CANNOT represent the sides of a triangle?

• 32, 34, 60
• 28, 30, 58
• 13, 20, 27
• 2, 4, 5

Multiple Select

Which of the following could NOT be the third side of a triangle with sides 35 and 14? Check all that apply.

• 21

• 48

• 26

• 35

• 14

Multiple Choice

If the measures of 2 sides of a triangle are 57 and 32, what is the LEAST possible measure of the third side if the measure is an integer?

• 25

• 26

• 88

• 89

Multiple Choice

If the longest side of the triangle was 10. Then the two shorter sides must have a sum that is ....?

• any length
• equal to 10
• greater than 10
• less than 10

Multiple Choice

Given are the lengths of two sides of a triangle. Find the range of lengths for the third side. 7 mm, 4 mm

• more than 3 but less than 11
• more than 11 but less than 3
• less than 3 but more than 11