Midsegments, 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?

Back

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

Front

How can you determine if a line is a perpendicular bisector?

Back

A line is a perpendicular bisector if it intersects a segment at its midpoint and forms right angles with the segment.

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 angles created by an angle bisector?

Back

To find the measures of the angles created by an angle bisector, divide the measure of the original angle by 2.

Front

If D, E, and F are midpoints of triangle ABC, what is the perimeter of triangle ABC if DE = 10?

Back

The perimeter of triangle ABC is 70, since the midsegment DE is half the length of side AC.

Front

What is the relationship between the lengths of the sides of a triangle and its midsegments?

Back

The lengths of the midsegments are always half the lengths of the sides of the triangle they are parallel to.

Front

If a line segment is divided into two equal parts, what is the length of each part if the total length is 16?

Back

Each part is 8, since 16 divided by 2 equals 8.

Front

How do you find the value of x in a triangle when given the lengths of the sides?

Back

Use the properties of triangles, such as the triangle inequality theorem, to set up equations and solve for x.