Perpendicular Bisectors of Triangles

Front

What is a perpendicular bisector?

Back

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

Front

What is the circumcenter of a triangle?

Back

The point where the perpendicular bisectors of the sides of a triangle intersect.

Front

If a triangle has sides of lengths 8, 15, and 17, what is the length of the perpendicular bisector from the vertex opposite the longest side?

Back

The length of the perpendicular bisector can be calculated using the formula: (1/2) * sqrt(2a^2 + 2b^2 - c^2), where a and b are the lengths of the other two sides, and c is the length of the side opposite the vertex.

Front

What is the relationship between the lengths of segments created by a perpendicular bisector?

Back

The segments created by a perpendicular bisector are equal in length.

Front

If AB = 10 and CD = 10, what is the length of the segment created by the perpendicular bisector of AB and CD?

Back

The length of the segment created by the perpendicular bisector is also 10.

Front

How do you find the circumcenter of a triangle?

Back

To find the circumcenter, construct the perpendicular bisectors of at least two sides of the triangle; their intersection point is the circumcenter.

Front

What is the significance of the circumcenter in a triangle?

Back

The circumcenter is equidistant from all three vertices of the triangle.

Front

If the lengths of two segments are equal, what can be said about their perpendicular bisector?

Back

The perpendicular bisector will also bisect the angle formed by the two segments.

Front

What is the formula for finding the length of a segment in a triangle using the perpendicular bisector?

Back

The length can be found using the Pythagorean theorem or the properties of similar triangles.

Front

If a triangle has a circumradius of 5, what is the maximum length of any side?

Back

The maximum length of any side of the triangle is less than or equal to 10 (twice the circumradius).