Answer:
angle measurements of 35, 35, and 110°
angle measurements of 40°, 60°, and 80°
Step-by-step explanation:
we know that
The length sides of a triangle must satisfy the Triangle Inequality Theorem and the sum of their interior angles must be equal to 180 degrees
Remember that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
That means, I can have more than one triangle with the same internal angles
so
<u><em>Verify each description</em></u>
case 1) side lengths of 6 ft, 8 ft, and 10 ft
Remember that
The <u><em>Triangle Inequality Theorem</em></u> states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
so
Applying the triangle inequality theorem
1) 6+8 > 10 ---> is true
2) 6+10 > 8 ---> is true
3) 8+10 > 6 ---> is true
therefore
The description describe only one triangle
case 2) angle measurements of 35, 35, and 110°
The sum of the interior angles is equal to 180 degrees
therefore
The description can describe more than one triangle, by similar triangles
case 3) angle measurements of 30°, 40, and 50°
The sum of the interior angles is not 180 degrees
therefore
The description is not a triangle
case 4) angle measurements of 40°, 60°, and 80°
The sum of the interior angles is equal to 180 degrees
therefore
The description can describe more than one triangle, by similar triangles
case 5) side lengths of 4 cm, 6 cm, and 9 cm
Remember that
The <u><em>Triangle Inequality Theorem</em></u> states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
so
Applying the triangle inequality theorem
1) 4+6 > 9 ---> is true
2) 4+9 > 6 ---> is true
3) 6+9 > 4 ---> is true
therefore
The description describe only one triangle
