Question

The letter or number on each side indicates the side's measure and the letter or number in the interior of each angle of each triangle indicates that angle's measure. Use your new conjectures to arrange the letters' values in order from greatest to the least.

Answer 1

Answer:

$\beta , \alpha , \gamma$

Step-by-step explanation:

Answer 2

Using conjectures comparing the relationship of angle measures of a triangle to its corresponding sides, the letters' values can be arranged from greatest to the least as:

• $\beta, \alpha, \gamma$ (Figure 1)
• c, b, a (Figure 2)
• v, w, x, z (Figure 3)
• a, b, c (Figure 4)

Recall the following conjectures about the relationship between the side lengths of a triangle and its angle measures:

• The largest angle measure is opposite to the longest side length in a triangle.
• The medium-sized angle measure is opposite to the medium-sized side length in a triangle.
• The smallest angle measure is opposite to the shortest side length in a triangle.

Using the above conjecture, let's arrange the given letters' values in the figures from greatest to the smallest.

Figure 1 (see attachment for image):

The longest side is 12 cm, and it is opposite to $\mathbf{\beta}$.

The medium-sized side length is 9 cm, and it opposite to $\alpha$

The shortest side is 5 cm, and it is opposite to $\gamma$

• Therefore, from greatest to the least, we would have:

$\beta, \alpha, \gamma$

Figure 2 (see attachment for image):

The largest angle measure is 68°, and it is opposite to c.

The medium-sized angle measure is 57°, and it opposite to b.

The smallest angle measure is 55°, and it is opposite to a.

• Therefore, from greatest to the least, we would have:

c, b, a

Figure 3 (see attachment for image):

v is opposite to 122°

w is opposite to 42°

x is opposite to 34°

z is opposite to 30°

• Therefore, from greatest to the least, we would have:

v, w, x, z

Figure 4 (see attachment for image):

a is opposite to 100°

b is opposite to 50°

c is opposite to 40°

• Therefore, from greatest to the least, we would have:

a, b, c

In summary, u

sing conjectures comparing the relationship of angle measures of a triangle to its corresponding sides, the letters' values can be arranged from greatest to the least as:

• $\beta, \alpha, \gamma$ (Figure 1)
• c, b, a (Figure 2)
• v, w, x, z (Figure 3)
• a, b, c (Figure 4)

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