5.3 &5.5 Triangle Theorems

Angle-Side Relationship (Fill in the notes!!!)

• Largest angle across from largest side

• Middle angle across from middle side

• Smallest angle across from smallest side

Multiple Choice

Select the largest angle.

• $$\angle G$$

• $$\angle F$$

• $$\angle H$$

Multiple Choice

Select the middle sized angle.

• $$\angle G$$

• $$\angle F$$

• $$\angle H$$

Multiple Choice

Select the smallest angle.

• $$\angle G$$

• $$\angle F$$

• $$\angle H$$

Multiple Choice

Which side is the longest? 

Hint: First find the missing angle.

• PQ

• QR

• RP

Multiple Choice

Which side is the middle length? 

Hint: First find the missing angle.

• PQ

• QR

• RP

Multiple Choice

Which side is the smallest length? 

Hint: First find the missing angle.

• PQ

• QR

• RP

Triangle Inequality Theorem (Fill in the notes!!!)

• To form a triangle:

• The sum of any two sides of a triangle must be greater than the third side

Multiple Choice

Which combination of sides forms a triangle?

• 1,1,2

• 3,5,7

Multiple Choice

Which combination of sides forms a triangle?

• 4,7,11

• 8,13,16

Pythagorean Inequalities (Fill in the notes!!!)

• If the square of the longest side is greater than the sum of the squares of the two shorter sides, then the triangle is obtuse.

• If the square of the longest side is less than the sum of the squares of the two shorter sides, then the triangle is acute.

• If the square of the longest side is equal to the sum of the squares of the two shorter sides, then the triangle is right angled at 𝐵.

Multiple Choice

Which combination of sides forms a RIGHT triangle?

• 9,13,17

• 5,12,13

• 9,11,14

Multiple Choice

Which combination of sides forms a ACUTE triangle?

• 9,13,17

• 5,12,13

• 9,11,14

Multiple Choice

Which combination of sides forms a OBTUSE triangle?

• 9,13,17

• 5,12,13

• 9,11,14