Use Theorem 5.9 about the angle-side relationships in triangles.
Example Solution:
Practice makes perfect
To begin, we can use the ruler to draw a triangle with the sides of different measures. Let's also measure the sides and label their length.
Now, we can use the following theorem.
If one side of a triangle
is longer than another side,
then the angle opposite the longer side
has a greater measure than the angle
opposite to the shorter side.
According to this theorem, to order the angles from largest to smallest, we can order the sides opposite to them. Let's do this!
BC>AC>AB
Now we need to find the angles opposite to these sides.
BC - ∠ A
AC - ∠ B
AB - ∠ C
Therefore, by the above theorem, we conclude the following.
m∠ A> m∠ B > m∠ C
