Triangles Unit Test

Question

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Question
Apply the Triangle Inequality Theorem to determine the possible whole number measures of the third side of a triangle if the first two sides measure 6 and 2. List them in ascending order.(2 points)
The measure of the third side could be
,
, or
.

Answer 1

The possible whole number measures of the third side of a triangle, using the Triangle Inequality Theorem, are:

- The measure of the third side should be greater than the difference of the first two sides but less than the sum of the first two sides.

In this case, the first two sides measure 6 and 2.

So, the third side should be greater than |6 - 2| = 4, and less than 6 + 2 = 8.

The possible whole number measures of the third side in ascending order are: 5, 6, 7.

Answer 2

A right triangle has acute angles measuring 2x+6 degrees and 3x−26 degrees. Use the Triangle Angle Sum Theorem to find the measures of the missing angles of the triangle.

Answer 3

The Triangle Angle Sum Theorem states that the sum of the measures of the angles in a triangle is always 180 degrees.

In this case, we have two of the angles: 2x + 6 degrees and 3x - 26 degrees.

To find the measure of the missing angle, we can use the fact that the sum of the measures of the angles in a triangle is always 180 degrees.

So, we can set up the following equation:

(2x + 6) + (3x - 26) + (missing angle) = 180

Combining like terms, we get:

5x - 20 + (missing angle) = 180

Now, we can solve for the missing angle by isolating it:

(missing angle) = 180 - 5x + 20
(missing angle) = 200 - 5x

Therefore, the measure of the missing angle is 200 - 5x degrees.