Perpendicular and 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 its length is half the length of that side.

Front

How do you find the length of a midsegment in a triangle?

Back

To find the length of a midsegment, measure the lengths of the two sides it connects, find their midpoints, and then use the formula: Length of midsegment = 1/2 * Length of the third side.

Front

What is the relationship between a perpendicular bisector and a segment?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle. Any point on the perpendicular bisector is equidistant from the endpoints of the segment.

Front

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

Back

To determine if a point lies on the perpendicular bisector, check if the distances from the point to the endpoints of the segment are equal.

Front

What is an angle bisector?

Back

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

Front

How do you find the measure of an angle using an angle bisector?

Back

To find the measure of an angle using an angle bisector, you can use the property that the angle bisector divides the angle into two equal parts.

Front

What is the significance of the midsegment theorem?

Back

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

Front

What is the relationship between angle bisectors and triangle properties?

Back

The angle bisectors of a triangle intersect at a point called the incenter, which is equidistant from all sides of the triangle.

Front

How do you solve for x in a triangle using midsegments?

Back

To solve for x using midsegments, set up an equation based on the midsegment theorem and solve for x.

Front

What is the definition of perpendicular lines?

Back

Perpendicular lines are lines that intersect at a right angle (90 degrees).