Triangles and Inequalities HW

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

Given two sides of a triangle measuring 7 mm and 4 mm, what is the range of possible lengths for the third side?

Back

The length of the third side must be more than 3 mm but less than 11 mm.

Front

What is the formula to find the range of the third side of a triangle given two sides a and b?

Back

The range for the third side c is: |a - b| < c < a + b.

Front

If one side of a triangle is 13 ft and another is 7 ft, what is the range for the third side?

Back

The length of the third side must be more than 6 ft but less than 20 ft.

Front

What does it mean if two angles are congruent in a triangle?

Back

If two angles are congruent, it means they have the same measure.

Front

How do you compare the measures of angles in a triangle?

Back

You can compare the measures of angles using the properties of triangles, such as the fact that the sum of the angles in a triangle is always 180 degrees.

Front

What is the relationship between the sides and angles of a triangle?

Back

In a triangle, the larger the side, the larger the opposite angle.

Front

Do the segment lengths 9, 12, and 15 form a right triangle?

Back

Yes, they do form a right triangle, as they satisfy the Pythagorean theorem: 9^2 + 12^2 = 15^2.

Front

What is the Pythagorean theorem?

Back

Front

What is the significance of the range of the third side in a triangle?

Back

The range of the third side ensures that a triangle can be formed with the given lengths, adhering to the Triangle Inequality Theorem.