Triangle Properties and Theorems

The video tutorial covers the fundamental concepts of triangle inequalities, including theorems and corollaries. It explains the relationship between angles and sides in triangles, the exterior angle theorem, and the triangle inequality theorem. The tutorial also provides examples to illustrate these concepts and their applications in determining possible side lengths of triangles.

What does the first theorem about triangles state regarding the largest angle?

• It is adjacent to the longest side.

• It is opposite the longest side.

• It is equal to the smallest angle.

• It is opposite the shortest side.

In a triangle with non-congruent sides, where is the smallest angle located?

• Next to the longest side

• Opposite the shortest side

• Adjacent to the largest angle

• Opposite the longest side

According to the second theorem, how does the measure of an exterior angle compare to its remote interior angles?

• It is the same as the sum of the remote interior angles.

• It is equal to one of the remote interior angles.

• It is smaller than both remote interior angles.

• It is greater than each of the remote interior angles.

What are the remote interior angles in relation to an exterior angle?

• Angles adjacent to the exterior angle

• Angles opposite the exterior angle

• Angles not connected to the exterior angle

• Angles equal to the exterior angle

What does the Triangle Inequality Theorem state about the sides of a triangle?

• The sum of any two sides must be less than the third side.

• The sum of any two sides must be greater than the third side.

• The sum of all three sides must be equal.

• The sum of any two sides must be equal to the third side.

If the sum of two sides of a triangle is not greater than the third side, what does this imply?

• The sides can form a triangle.

• The sides cannot form a triangle.

• The triangle is isosceles.

• The triangle is equilateral.

According to the corollary, what must the length of the third side of a triangle be?

• Equal to the sum of the other two sides

• Less than the difference of the other two sides

• Greater than the sum of the other two sides

• Greater than the difference and less than the sum of the other two sides

If two sides of a triangle are 3 cm and 5 cm, what is the range for the third side?

• Between 2 cm and 8 cm

• Between 1 cm and 9 cm

• Between 3 cm and 5 cm

• Between 4 cm and 10 cm

Given the lengths 6, 7, and 12, can these form a triangle?

• Yes, because 6 + 7 > 12

• Yes, because 6 + 7 = 12

• No, because 6 + 7 < 12

• No, because 6 + 7 = 12

Why can't the lengths 5, 6, and 12 form a triangle?

• Because 5 + 6 < 12

• Because 5 + 6 > 12

• Because 5 + 6 = 12

• Because 5 + 6 > 11