Triangle Inequality Theorem and Triangle Sum

​More Triangle Theorem Stuff

​Dr. Tom Giles

​Additional Triangle Theorems

Triangle Inequality Theorem

Ordering Angles & Sides of a Triangle

Exterior Angle Inequality Theorem

CPCTC

​Triangle Inequality Theorem
The sum of any two sides of a triangle is greater than or equal to the third side

Multiple Choice

State if the three numbers can be measures of the sides of a triangle.
$$10,18,12$$  

• Yes

• No

Multiple Choice

State if the three numbers can be measures of the sides of a triangle.
$$8,10,20$$  

• Yes

• No

Multiple Choice

State if the three numbers can be measures of the sides of a triangle.
$$18,7,10$$  

• Yes

• No

Multiple Choice

State if the three numbers can be measures of the sides of a triangle.
$$11,1,12$$  

• Yes

• No

Multiple Choice

Two sides of a triangle have the following measures. Find the range of possible measure for the third side.
$$12,12$$  

• $$1<x<24$$  

• $$4<x<24$$  

• $$4<x<23$$  

• $$0<x<24$$  

Multiple Choice

Two sides of a triangle have the following measures. Find the range of possible measure for the third side.
$$9,6$$  

• $$5<x<14$$  

• $$3<x<15$$  

• $$3<x<14$$  

• $$4<x<14$$  

Multiple Choice

In triangle ABC, the length of side AB is 10 inches and the length of side BC is 17 inches.  Which of the following could be the length of side AC?

• 16 inches
• 5 inches
• 32 inches
• 29 inches

​Ordering Sides & Angles of Triangles

Multiple Choice

Identify the shortest side measure.

• QP
• QM
• MP

Multiple Choice

Identify the longest side measure.

• AC
• BA
• BC

Multiple Choice

Identify the smallest angle.

• ∠A
• ∠B
• ∠C

Multiple Choice

Identify the smallest angle.

• ∠K
• ∠L
• ∠M

Multiple Choice

Identify the largest angle.

• ∠N
• ∠Q
• ∠P

Multiple Choice

Identify the longest side measure.

• LM
• MQ
• LQ

Multiple Choice

Name the smallest angle in this triangle.

• ∠A
• ∠B
• ∠C

Multiple Choice

Name the angles from LARGEST to SMALLEST

• R, S, T
• S, T, R
• S, R, T
• T, S, R

Multiple Choice

Order the angles from greatest to least. 

• a, b ,c
• a , c, b
• c , b , a
• b , c , a

Multiple Choice

List the side measures in order, shortest to longest.

• QM, QP, MP
• MQ, MP, QP
• MP, MQ, QP

​Exterior Angle Inequality Theorem
The measure of any exterior angle of a triangle is greater than both of the non-adjacent interior angles

Multiple Choice

Which of ∠2, ∠4, and ∠6 has the largest measure?

• ∠2

• ∠4

• ∠6

Multiple Choice

Which of ∠4, ∠5, and ∠1 has the largest measure?

• ∠4

• ∠5

• ∠1

Multiple Choice

Which of ∠1, ∠7, and ∠2 has the largest measure?

• ∠1

• ∠7

• ∠2

Multiple Choice

Using the figure, choose the correct symbol to be used.

∠7 _____ ∠2

• <

• >

• =

Multiple Choice

Using the figure, choose the correct symbol to be used.

∠6 _____ ∠8

• <

• >

• =

Multiple Choice

Using the figure, choose the correct symbol to be used.

∠4 _____ ∠8

• <

• >

• =

CPCTC
Corresponding Parts of Congruent Triangles are Congruent
If two triangles are congruent, then all corresponding sides & angles of those triangles are congruent to each other.

​Whadda Ya Think?