Midsegments and Perpendicular/Angle Bisectors

Front

What is the Midsegment Theorem?

Back

The Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side.

Front

What does the Perpendicular Bisector Theorem state?

Back

The Perpendicular Bisector Theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Front

What is a midsegment in a triangle?

Back

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

Front

How do you find the length of a midsegment?

Back

The length of a midsegment is half the length of the third side of the 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

If point C lies on the perpendicular bisector of segment AB, what can we conclude about distances AC and BC?

Back

If point C lies on the perpendicular bisector of segment AB, then AC = BC.

Front

What is the relationship between a midsegment and the sides of a triangle?

Back

A midsegment is parallel to one side of the triangle and its length is half the length of that side.

Front

What is the converse of the Perpendicular Bisector Theorem?

Back

The converse of the Perpendicular Bisector Theorem states that if a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of that segment.

Front

What is an angle bisector?

Back

An angle bisector is a ray that divides an angle into two equal angles.

Front

How can you determine if a point is on the perpendicular bisector of a segment?

Back

To determine if a point is on the perpendicular bisector of a segment, check if it is equidistant from the endpoints of the segment.