Angle Bisector
Is a median, altitude, angle bisector, or perpendicular bisector shown?
An angle bisector is a line, ray or line segment that divides an angle into two equal parts or halves. The point where the bisector meets the angle is called the vertex of the angle.
To construct an angle bisector, there are several steps that can be taken. Let us consider this in a right-angled triangle with hypotenuse AB, and right angle C.
1. Draw the triangle and label the vertices A, B and C.
2. Draw a straight line from vertex C to hypotenuse AB, such that the line is perpendicular to AB. Let’s label the point where the line intersects AB as D.
3. Measure the lengths of AC and BC and find their sum.
4. Bisect the sum obtained in step 3, from point D, to the opposite side of the triangle. This is done by drawing a straight line from point D to the opposite vertex (point C).
5. The line that is formed from D to the opposite vertex (point C) is the bisector of the angle formed by the two adjacent sides of the triangle.
The angle bisector theorem states that the angle bisector of a triangle divides the opposite side (or segment) of that triangle into two parts that are proportional to the adjacent sides. This theorem can be used to find missing side lengths in a triangle when other side lengths are known.
In summary, constructing an angle bisector involves drawing a line that divides an angle into two equal parts, and the angle bisector theorem is a useful tool for finding missing side lengths in a triangle.
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