Perpendicular Bisector Theorem

Front

What is the Perpendicular Bisector Theorem?

Back

The Perpendicular Bisector Theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Front

Define 'perpendicular bisector'.

Back

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

Front

If point P is on the perpendicular bisector of segment AB, what can be said about the distances PA and PB?

Back

PA = PB; point P is equidistant from points A and B.

Front

How do you find the midpoint of a segment?

Back

To find the midpoint of a segment with endpoints (x1, y1) and (x2, y2), use the formula: Midpoint = ((x1 + x2)/2, (y1 + y2)/2).

Front

What is the relationship between the slopes of two perpendicular lines?

Back

The slopes of two perpendicular lines are negative reciprocals of each other.

Front

If line segment AB has endpoints A(2, 3) and B(6, 7), what is the length of AB?

Back

Length of AB = √((x2 - x1)² + (y2 - y1)²) = √((6 - 2)² + (7 - 3)²) = √(16 + 16) = √32 = 4√2.

Front

What is the significance of the Perpendicular Bisector Theorem in triangle construction?

Back

It helps in constructing the circumcenter of a triangle, which is the point where the perpendicular bisectors of the sides intersect.

Front

If a triangle has sides of lengths 6, 8, and 10, what can be said about it?

Back

It is a right triangle, as it satisfies the Pythagorean theorem: 6² + 8² = 10².

Front

What is the formula for the distance between two points (x1, y1) and (x2, y2)?

Back

Distance = √((x2 - x1)² + (y2 - y1)²).

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 the endpoints of the segment are equal.