Relationships with triangles

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

In triangle ABC, if AB = 10 inches and BC = 17 inches, what could be the possible range for side AC?

Back

According to the Triangle Inequality Theorem, AC must be greater than |AB - BC| and less than AB + BC. Therefore, AC must be greater than |10 - 17| = 7 inches and less than 10 + 17 = 27 inches. So, 7 < AC < 27.

Front

How do you determine the longest side of a triangle?

Back

The longest side of a triangle is opposite the largest angle. To find it, compare the measures of the angles.

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. Conversely, the smaller the side, the smaller the opposite angle.

Front

What is the formula for calculating the area of a triangle?

Back

The area of a triangle can be calculated using the formula: Area = 1/2 * base * height.

Front

How can you identify the shortest side of a triangle?

Back

The shortest side of a triangle is opposite the smallest angle. To identify it, compare the measures of the angles.

Front

What is the significance of the angles in a triangle?

Back

The angles in a triangle determine the shape and type of triangle (acute, right, obtuse) and are crucial for applying the Triangle Inequality Theorem.

Front

What is an acute triangle?

Back

An acute triangle is a triangle where all three angles are less than 90 degrees.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle equal to 90 degrees.

Front

What is an obtuse triangle?

Back

An obtuse triangle is a triangle that has one angle greater than 90 degrees.