ORDERING TRIANGLE SIDES AND ANGLES

Angle Side Relationship

Example 1 :

In ΔGEF below, order the sides from shortest to longest.

Answer :

Order the angles from smallest to largest :

55°, 62°, 63°

The side opposite to the smallest angle is the shortest side and the side opposite to the largest angle is the longest side. 

side opposite to 55° ----> GE

side opposite to 62° ----> GF

side opposite to 63° ----> EF

Order of the sides from shortest to longest :

GE, GF, EF

Example 2 :

In ΔABC below, order the sides from longest to shortest.

Answer :

In ΔABC above,

m∠A + m∠B + m∠C = 180°

Substitute m∠B = 102° and m∠C = 46°.

m∠A + 102° + 46° = 180°

m∠A + 148° = 180°

Subtract 148° from each side.

m∠A = 32°

Order the angles from smallest to largest :

32°, 46°, 102°

side opposite to 102° ----> AC

side opposite to 46° ----> AB

side opposite to 32° ----> BC

Order of the sides from longest to shortest : 

AC, AB, BC

Example 3 :

In ΔEFD below, order the sides from shortest to longest.

Answer :

m∠E = 48° and the remaining two angles m∠F and m∠D are equal, that is 66°. 

side opposite to m∠E ----> FD

side opposite to m∠F ----> ED

side opposite to m∠D ----> EF

In ΔEFD above, the shortest side is FD and the remaining two sides ED and EF are equal in length.

Example 4 :

In ΔJKL below, order the angles from smallest to greatest.

Answer :

Order the sides from shortest to longest :  

14 yd, 16 yd, 18 yd

The angle opposite to the shortest side is the smallest angle and the side opposite to the longest side is the largest angle.

angle opposite to the side 14 yd long ----> ∠J

angle opposite to the side 16 yd long ----> ∠K

angle opposite to the side 18 yd long ----> ∠L

Order of the angles from smallest to largest :

∠J, ∠K, ∠L

Example 5 :

In ΔKLM below, KL = 18 cm, LM = 20 cm and KM = 13 cm. Order the angles from largest to smallest.

Answer :

Draw ΔKLM with the given measures.

Order the sides from longest to shortest :

20 cm, 18 cm, 13 cm

angle opposite to the side 20 cm long ----> ∠K

angle opposite to the side 18 cm long ----> ∠M

angle opposite to the side 13 cm long ----> ∠L

Order of the angles from smallest to largest :

∠K, ∠M, ∠L

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