Exploring the Triangle Inequality Theorem

The video tutorial covers key geometry concepts, starting with the definitions of median and altitude in triangles. It then explains the triangle inequality theorem, providing examples to illustrate how to determine if given side lengths can form a triangle. The tutorial also covers how to find the range of possible lengths for a triangle's third side. Finally, it discusses how to order the angles and sides of a triangle based on their measurements.

What is a median in a triangle?

• A segment that bisects an angle of a triangle.

• A segment that connects the vertex of a triangle to the opposite side so that it is perpendicular to that side.

• A segment that is parallel to one side of the triangle.

• A segment that connects the vertex of a triangle to the midpoint of the opposite side.

What is the altitude in a triangle?

• A segment that connects the vertex of a triangle to the midpoint of the opposite side.

• A segment that connects the vertex of a triangle to the opposite side so that it is perpendicular to that side.

• A segment that bisects an angle of a triangle.

• A segment that is parallel to one side of the triangle.

According to the Triangle Inequality Theorem, when do three side lengths form a triangle?

• When the sum of the two larger sides is less than the third side.

• When the sum of the two smaller sides is greater than the third side.

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

• When the difference of any two sides is greater than the third side.

If the two smaller sides of a triangle are 8 and 17, and the third side is 24, do these sides form a triangle?

• No, because 8 + 17 is not equal to 24.

• Yes, because 8 + 17 is equal to 24.

• No, because 8 + 17 is less than 24.

• Yes, because 8 + 17 is greater than 24.

What is the range of possible values for the third side if the other two sides are 22 and 14?

• Between 14 and 22

• Between 8 and 36

• Between 22 and 36

• Between 8 and 22

If a triangle has sides of 15 and 27, which of the following could be the third side?

• 50

• 34

• 10

• 5

In a triangle, which angle is opposite the shortest side?

• The smallest angle

• The obtuse angle

• The largest angle

• The right angle

If the sides of a triangle are 17m, 20m, and 24m, which angle is the largest?

• The angle opposite the 17m and 20m sides

• The angle opposite the 17m side

• The angle opposite the 20m side

• The angle opposite the 24m side

If the angles of a triangle are 35°, 42°, and 103°, which side is the longest?

• The side opposite the 35° and 42° angles

• The side opposite the 103° angle

• The side opposite the 42° angle

• The side opposite the 35° angle

If the angles of a triangle are 82°, 54°, and 44°, which side is the shortest?

• The side opposite the 44° angle

• The side opposite the 54° angle

• The side opposite the 82° and 54° angles

• The side opposite the 82° angle