5.1 Perpendicular and Angle Bisectors

Front

What is a perpendicular bisector?

Back

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

Front

What is an angle bisector?

Back

A line that divides an angle into two equal angles.

Front

How do you find the length of a segment using the perpendicular bisector?

Back

Use the midpoint formula and the distance formula to calculate the lengths.

Front

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

Back

Any point on the perpendicular bisector is equidistant from the endpoints of the segment.

Front

What is the significance of the angle bisector in triangle geometry?

Back

The angle bisector divides the opposite side into segments that are proportional to the adjacent sides.

Front

If AD = 8 and BC = 12, what is the ratio of AD to BC?

Back

The ratio of AD to BC is 2:3.

Front

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

Back

Check if the distances from the point to both endpoints of the segment are equal.

Front

What is the formula for finding the midpoint of a segment with endpoints (x1, y1) and (x2, y2)?

Back

Midpoint = ((x1 + x2)/2, (y1 + y2)/2).

Front

If a triangle has angles of 30°, 60°, and 90°, what is the relationship of the angle bisectors?

Back

The angle bisector of the 30° angle will divide it into two 15° angles.

Front

What is the theorem related to the angle bisector and the opposite side of a triangle?

Back

The Angle Bisector Theorem states that the ratio of the two segments created on the opposite side is equal to the ratio of the other two sides.