Angle Bisectors

Front

What is an angle bisector?

Back

An angle bisector is a line or ray that divides an angle into two equal parts.

Front

What is the Angle Bisector Theorem?

Back

The Angle Bisector Theorem states that the ratio of the lengths of the two segments created by an angle bisector on the opposite side is equal to the ratio of the lengths of the other two sides of the triangle.

Front

If angle A is bisected, what can be said about angles A1 and A2?

Back

Angles A1 and A2 are equal, where A1 and A2 are the two angles formed by the angle bisector.

Front

In triangle ABC, if AB = 6, AC = 8, and the angle bisector of angle A intersects BC at D, what is the ratio BD:DC?

Back

The ratio BD:DC is 6:8 or 3:4.

Front

How do you find the length of an angle bisector in a triangle?

Back

The length of an angle bisector can be found using the formula: l = (2bc)/(b+c) * cos(A/2), where A is the angle being bisected, and b and c are the lengths of the other two sides.

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 two segments that are proportional to the lengths of the other two sides.

Front

If the angles of a triangle are 30°, 60°, and 90°, what is the measure of the angle bisector of the 90° angle?

Back

The angle bisector of the 90° angle will create two angles of 45° each.

Front

What is the significance of angle bisectors in triangle construction?

Back

Angle bisectors are significant in triangle construction as they help in finding the incenter, which is the center of the inscribed circle.

Front

How can you use angle bisectors to solve for unknown angles in a triangle?

Back

You can use angle bisectors to set up equations based on the property that the angles created are equal, allowing you to solve for unknown angles.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect, and it is equidistant from all three sides.