a.
To find: the common property of the red figures.
a.
Answer to Problem 11CE
Opposite sides are equal and parallel in all the red figures.
Explanation of Solution
Given:
The new quadrilaterals are formed by joining the midpoints of the sides of the quadrilaterals.
The red figures are made by joining the midpoints of the sides of the quadrilaterals.
The common property of the formed quadrilaterals is that opposite sides are equal and parallel in all cases.
Conclusion:
Therefore, the common property is that the opposite sides are equal and parallel.
b.
To prove: that opposite sides are equal and parallel.
b.
Explanation of Solution
Given:
The new quadrilaterals are formed by joining the midpoints of the sides of the quadrilaterals.
Take one figure from the above four figures.
Join
In
By Midpoint Theorem,
and
In
By Midpoint Theorem,
and
From equation (ii) and equation (iv),
Similarly by joining
Similarly the same can be proven for other figures.
Conclusion:
Therefore, the opposite sides of red figures are equal and parallel.
Chapter 5 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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