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Magazine Chapter 5: Q. 7 (page 186)
The following figure is rhombus
a. Fbeing equidistant from E and Gmust lie on the __ of.
b. Hbeing equidistant from E and Gmust lie on the __ of.
c. From (a) and (b) you can deduce that is the __ of.
d. state the theorem of this section that you have just proved.
Short Answer
a. Perpendicular bisector.
b. Perpendicular bisector.
c. Perpendicular bisector.
d. According to this theorem, if a point is equidistant from the endpoints of the segment, then the point lies on the perpendicular bisector of a segment.
Step by step solution
a. Step 1- Check the figure.
Consider the figure.
Step 2- Step description.
According to theorem, if a point is equidistant from the endpoints of the segment, then the point lies on the perpendicular bisector of a segment.
Step 3- Step description.
Since F is equidistant from E and G .
Therefore, must lie on perpendicular bisector of .
Therefore, the answer is perpendicular bisector.
b. Step 1- Check the figure.
Consider the figure.
Step 2- Step description.
According to theorem, if a point is equidistant from the endpoints of the segment, then the point lies on the perpendicular bisector of a segment.
Step 3- Step description.
Since F is equidistant from and .
Therefore, must lie on perpendicular bisector of .
Therefore, the answer is perpendicular bisector.
d. Step 1- Check the figure.
Consider the figure.
Step 2- Step description.
According to theorem, if a point is equidistant from the endpoints of the segment, then the point lies on the perpendicular bisector of a segment.
Step 3- Step description.
Therefore, the theorem, if a point is equidistant from the endpoints of the segment, then the point lies on the perpendicular bisector of a segment.
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