Triangle Vocabulary and Theorems Exploration

This video tutorial covers various triangle-related concepts, including the triangle inequality theorem, medians, orthocenter, exterior angle theorem, and angle-side relationships. It also explains the geometric mean in right triangles and classifies triangles by side lengths and angles. The video concludes with a call to action to subscribe for more educational content.

What does the triangle inequality theorem state about the sides of a triangle?

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

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

• The sum of all three sides is equal.

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

What is a median in a triangle?

• A line perpendicular to one side.

• A line bisecting an angle of the triangle.

• A line segment joining the midpoints of two sides.

• A line segment joining a vertex to the midpoint of the opposite side.

Where do the medians of a triangle intersect?

• At the centroid

• At the circumcenter

• At the orthocenter

• At the incenter

What does the exterior angle theorem state?

• The exterior angle is equal to the sum of the two opposite interior angles.

• The exterior angle is less than each of the interior angles.

• The exterior angle is greater than the sum of the two adjacent interior angles.

• The exterior angle is equal to the sum of the two adjacent interior angles.

Which side of a triangle is the longest when the opposite angle is the largest?

• All sides are equal

• The side opposite the smallest angle

• The side opposite the largest angle

• The side adjacent to the largest angle

In a right triangle, what does the geometric mean relate?

• The area and the perimeter

• The hypotenuse and one leg

• The altitude and the segments it divides the hypotenuse into

• The two legs

What type of triangle has all sides of different lengths?

• Equilateral

• Isosceles

• Scalene

• Right

Which triangle has angles all less than 90 degrees?

• Obtuse

• Acute

• Right

• Equiangular

What type of triangle has one angle exactly 90 degrees?

• Right

• Equilateral

• Obtuse

• Acute

Which triangle has all angles equal to 60 degrees?

• Acute

• Scalene

• Equilateral

• Isosceles