Mid-Segment Lengths in Triangles

The video tutorial covers the concepts of parallel lines and proportional parts, focusing on the triangle proportionality theorem and the triangle mid-segment theorem. It explains how to set up and solve proportions within triangles and with three parallel lines, providing examples and exercises to reinforce understanding.

What does the triangle proportionality theorem allow you to do when a segment is parallel to one side of a triangle?

• Determine the type of triangle

• Find the angles of the triangle

• Set up proportions between the sides

• Calculate the area of the triangle

If AE is parallel to BC in a triangle, which of the following is a valid proportion?

• AB/BC = ED/DC

• AB/ED = BC/DC

• AB/BC = DC/ED

• AB/ED = DC/BC

When setting up proportions in a triangle, what must you ensure?

• The segments are congruent

• The order of terms is consistent

• The angles are equal

• The triangle is isosceles

Which of the following is NOT a valid proportion for a triangle with a parallel segment?

• 9/21 = 6/x

• x/9 = 6/21

• 9/x = 21/6

• 9/6 = 21/x

What is the triangle mid-segment theorem primarily concerned with?

• The angles of a triangle

• The area of a triangle

• The congruence of sides

• The relationship between a mid-segment and the base

In the triangle mid-segment theorem, what is the length of the mid-segment compared to the base?

• Equal to the base

• Twice the base

• Half the base

• Three times the base

If a mid-segment is 17 units long, what is the length of the base?

• 8.5 units

• 17 units

• 68 units

• 34 units

What is a key characteristic of a mid-segment in a triangle?

• It is perpendicular to the base

• It bisects the base

• It is parallel to the base

• It is equal in length to the base

What is the length of the mid-segment if the base is 34?

• 17

• 34

• 68

• 51

If a mid-segment is 18, what is the length of the base?

• 18

• 9

• 72

• 36