Triangle Midsegment / Proportionality

Front

What is a midsegment in a triangle?

Back

A midsegment is a segment that connects the midpoints of two sides of a triangle, and it is parallel to the third side.

Front

What is the relationship between the lengths of a midsegment and the side it is parallel to?

Back

The length of a midsegment is half the length of the side it is parallel to.

Front

If segment QR is a midsegment of triangle WUV, and UV = 16, what is the length of QR?

Back

8 (QR is half the length of UV).

Front

What does it mean for segments to be proportional?

Back

Segments are proportional if the ratios of their lengths are equal.

Front

If CB / DM = AC / ?, what is the missing segment if CB = 4, DM = 2, and AC = 8?

Back

AD = 4 (using cross-multiplication to solve the proportion).

Front

What is the Triangle Midsegment Theorem?

Back

The Triangle Midsegment Theorem states that a midsegment of a triangle is parallel to one side of the triangle and its length is half the length of that side.

Front

How do you find the length of a midsegment if you know the lengths of the two sides it connects?

Back

The length of the midsegment is the average of the lengths of the two sides it connects.

Front

If segment BD = 10, what is the length of segment AD if AD is a midsegment?

Back

AD = 10 (AD is equal to BD if it is a midsegment connecting the midpoints of the other two sides).

Front

What is the significance of midpoints in triangles?

Back

Midpoints are important because they help in forming midsegments, which are crucial for understanding triangle properties and proportionality.

Front

If segment FG is parallel to segment EF, what can be said about the triangles formed?

Back

The triangles formed are similar by the Basic Proportionality Theorem (or Thales' theorem).