Perpendicular Bisectors and Midsegments of a Triangle

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

Front

What is a midsegment of a triangle?

Back

A midsegment of a triangle is a segment that connects the midpoints of two sides of the triangle.

Front

How does the length of a midsegment compare to the lengths of the sides of the triangle?

Back

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

Front

If AC = 42, what is the length of the midsegment DF connecting the midpoints of AB and AC?

Back

DF = 21, which is half of AC.

Front

What is the relationship between the perpendicular bisector and the triangle's vertices?

Back

The perpendicular bisector of a side of a triangle passes through the midpoint of that side and is equidistant from the triangle's vertices.

Front

If XZ = 22, what is the length of BC if BC is the side opposite to the midsegment?

Back

BC = 44, as the midsegment is half the length of the side it is parallel to.

Front

How do you find the length of a side of a triangle using its midsegment?

Back

To find the length of a side, multiply the length of the midsegment by 2.

Front

What is the significance of the point where the perpendicular bisectors of a triangle intersect?

Back

The intersection point of the perpendicular bisectors is called the circumcenter, which is equidistant from all three vertices of the triangle.

Front

If the lengths of two sides of a triangle are known, how can you find the length of the third side using the midsegment?

Back

Use the midsegment's length to determine the relationship between the sides, applying the triangle inequality theorem.

Front

What is the triangle inequality theorem?

Back

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.