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Magazine Chapter 4: Q. 20 (page 161)
and are congruent right triangles with common hypotenuse . Write the theorem that allows you to conclude that point lies on the bisector of .
Short Answer
The theorem that conclude that point lies on the bisector of is that if a point is equidistant from the sides of an angle, then the point will lie on the bisector of the angle.
Step by step solution
- Definition of angle bisector.
The angle bisector of a given angle is the ray or segment that divides the given angle into two equal angles.
- Consider the diagram.
The figure is:
As, andare the congruent triangles, therefore .
That implies the point is equidistant from the points D and C .
Therefore, lies on the bisector of .
- Write the theorem that conclude that point lies on the bisector of .
The theorem that conclude that point lies on the bisector of is that if a point is equidistant from the sides of an angle, then the point will lie on the bisector of the angle.
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