Geo 5-3 Inequalities in One Triangle

The angles in order from least to greatest are:

​ (a)   , ​ (b)   ,​ (c)  

• ∠C
• ∠B
• ∠A

List the sides from Longest to Shortest:

​ ​ (a)   , ​ (b)   , ​ ​ (c)  

Which side is the longest?

List the angles of ▲TVX in order from smallest to the largest.

• ∠T

• ∠X

• ∠V

Answer explanation

Remember that the smallest angle is opposite the shortest side and the largest angle is opposite the longest side.

The opposite side of ∠V is TX.  The opposite side of ∠T is VX.  The opposite side of ∠X is TV

List the angles of ▲PQR in order from smallest to largest.

• ∠Q

• ∠P

• ∠R

Answer explanation

Remember that the smallest angle is opposite the shortest side and the largest angle is opposite the longest side.

∠P is opposite of the side marked 9.1

∠Q is opposite of the side marked 7.5

∠R is opposite of the side marked 8.8

List the sides of ▲RST in order from shortest to longest.

Answer explanation

Remember that the longest side is opposite the largest angle and the shortest side is opposite the smallest angle.

Side ST is opposite ∠R

Side RS is opposite ∠T

Side RT is opposite ∠S

What is the measure of ∠F?

Answer explanation

Use the fact that the sum of the angles of a triangle add up to 180°.

The measure of ∠F = 180 - 45 - 56

List the sides of ▲FGH from shortest to longest.

Answer explanation

Remember the longest side is opposite the biggest angle and the shortest side is opposite the smallest angle.

∠F is across from side GH

∠H is across from side FG

∠G is across from side FH

List the angles (from 2-10) that are

Groups:

(a) Less than m∠1

,

(b) NOT less than m∠1

• ∠6

• ∠2

• ∠10

• ∠4

• ∠7

• ∠5

• ∠3

• ∠9

List the angles (from 2-10) that are less than m∠1

Groups:

(a) Less than m∠1

,

(b) NOT Less than m∠1

• ∠6

• ∠8

• ∠3

• ∠5

• ∠7

• ∠4

• ∠2