11.15.24 Perp. Bisectors, Circumcenter & Ineq. of Triangles

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is 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 circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect, and it is equidistant from the vertices of the triangle.

Front

How do you find the length of a segment using the circumcenter?

Back

To find the length of a segment from the circumcenter to a vertex, you can use the distance formula or geometric properties of the triangle.

Front

What is the relationship between angle bisectors and the angles they divide?

Back

An angle bisector divides an angle into two equal angles.

Front

If angle ABC measures 98 degrees and BD is an angle bisector, what are the measures of angles ABD and DBC?

Back

Both angles ABD and DBC measure 49 degrees.

Front

What is the significance of the circumradius in a triangle?

Back

The circumradius is the radius of the circumcircle, which is the circle that passes through all three vertices of the triangle.

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 the inequality of triangles?

Back

The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

What is the smallest angle in a triangle?

Back

The smallest angle in a triangle is opposite the shortest side.

Front

How do you find the circumcenter in a triangle?

Back

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