Angle Bisector and Perpendicular Bisectors part CW

Front

What is an angle bisector?

Back

A line, segment, or ray that divides an angle into two equal parts.

Front

What is a perpendicular bisector?

Back

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

Front

If angle A measures 60 degrees, what is the measure of each angle formed by the angle bisector?

Back

30 degrees each.

Front

What is the relationship between the angle bisector and the opposite side in a triangle?

Back

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

Front

In triangle ABC, if AD is the angle bisector of angle A, what can be said about the lengths of BD and DC?

Back

BD/DC = AB/AC.

Front

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

Back

Use the ratio of the lengths of the other two sides of the triangle.

Front

What is the significance of the circumcenter in relation to perpendicular bisectors?

Back

The circumcenter is the point where the perpendicular bisectors of a triangle intersect, and it is equidistant from all three vertices.

Front

If a triangle has sides of lengths 5, 12, and 13, what type of triangle is it?

Back

It is a right triangle.

Front

What is the formula for finding the length of the angle bisector in a triangle?

Back

l = (2ab)/(a+b) * cos(C/2), where a and b are the lengths of the sides and C is the angle between them.

Front

If the lengths of two sides of a triangle are 8 and 6, and the angle between them is 60 degrees, what is the length of the angle bisector?

Back

Approximately 7.21 units.