Midsegments and Perpendicular/Angle Bisectors

Front

What is a midsegment in a triangle?

Back

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

Front

What does the Midsegment Theorem state?

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 is the Angle Bisectors Theorem?

Back

The Angle Bisectors Theorem states that if a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.

Front

What is an angle bisector?

Back

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

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

How do you find the length of a midsegment?

Back

To find the length of a midsegment, measure the lengths of the two sides it connects and apply the Midsegment Theorem.

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 the significance of the perpendicular bisector in a triangle?

Back

The perpendicular bisector of a side of a triangle is the locus of points equidistant from the endpoints of that side.

Front

How can you determine if a line is an angle bisector?

Back

A line is an angle bisector if it divides the angle into two equal angles.

Front

What is the Converse of the Angle Bisector Theorem?

Back

The Converse of the Angle Bisector Theorem states that if a point is equidistant from the sides of an angle, then it lies on the angle bisector.