The construction of each figure.
Answer to Problem 39PPS
It is a rhombus.
Explanation of Solution
Given:
The figure to be constructed is a rhombus.
Calculation:
In order to construct a rhombus, follow these steps:
- Draw a perpendicular bisector of a line segment.
- Keep the compass at the midpoint of that line segment.
- Using the same compass, locate a point on the perpendicular bisector above and below the line segment.
- Join the two end points of the line segments with the two points on the perpendicular bisector to draw a quadrilateral.
The figure will be:
If in a quadrilateral, the diagonals bisect each other, it is a parallelogram.
According to Rhombi Theorem, if the diagonals of a parallelogram are perpendicular, then it is a rhombus.
The diagonals in the above drawn figure bisect each other, hence it is a parallelogram.
Also, the diagonals are perpendicular, according to the Rhombi Theorem, the figure is a rhombus.
Chapter 6 Solutions
Geometry, Student Edition
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