Midsegments and Perpendicular/Angle Bisectors

Front

What is a midsegment in a triangle?

Back

A midsegment is a line segment that connects the midpoints of two sides of a triangle. It is parallel to the third side and half its length.

Front

State 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 its length is half the length of the third side.

Front

What is a perpendicular bisector?

Back

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

Front

What is the Angle Bisector Theorem?

Back

The Angle Bisector Theorem states that the ratio of the lengths of the two segments created by an angle bisector is equal to the ratio of the lengths of the two sides of the triangle that form the angle.

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 then use the formula: Length of midsegment = (1/2) * Length of the third 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 the relationship between angle bisectors and triangle sides?

Back

Angle bisectors divide the opposite side into segments that are proportional to the lengths of the other two sides of the triangle.

Front

If a triangle has sides of lengths 6, 8, and 10, what is the length of the midsegment connecting the sides of lengths 6 and 8?

Back

The length of the midsegment is 5, which is half the length of the third side (10).

Front

What is the definition of a perpendicular bisector in terms of distance?

Back

A perpendicular bisector is the locus of points that are equidistant from the endpoints of a segment.

Front

How can you determine if a point lies on the angle bisector of an angle?

Back

A point lies on the angle bisector if it is equidistant from the two sides of the angle.