Perpendicular and Angle Bisectors

Front

What is a perpendicular bisector?

Back

A line, segment, or ray that passes through the midpoint of a side and creates a 90-degree angle with that side.

Front

What is an angle bisector?

Back

A line that divides an angle into two equal parts.

Front

Define median in a triangle.

Back

A line segment joining a vertex to the midpoint of the opposite side.

Front

What is the relationship between perpendicular bisectors and triangles?

Back

The perpendicular bisectors of a triangle intersect at a point called the circumcenter, which is equidistant from the vertices.

Front

What is the circumcenter of a triangle?

Back

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

Front

How do you find the length of a segment using the Pythagorean theorem?

Back

For a right triangle, the length of the hypotenuse can be found using the formula a² + b² = c², where c is the hypotenuse.

Front

What is the significance of the angle bisector theorem?

Back

It states that the ratio of the lengths of the two segments created by the angle bisector on the opposite side is equal to the ratio of the other two sides of the triangle.

Front

If a triangle has sides of lengths 3, 4, and 5, what type of triangle is it?

Back

It is a right triangle, as it satisfies the Pythagorean theorem.

Front

What is the length of DC if it is given as 4?

Back

DC = 4.

Front

What is the length of HG if it is given as 14?

Back

HG = 14.