Solution Exercise 4.31.
Definition of Term Commonly Used
in Mathematics:
Clearly – I do not want to write down
all the steps.
Exercise 4.31. (a) State the dual of Theorem 4.10.
Dual of Theorem 4.10. If a, b, c and a', b', c' are distinct elements in pencils of lines with distinct centers P and P', respectively, then there exists a projectivity such that abc is projectively related to a'b'c'.
(b) Assume a, b, c are elements of a pencil with center P and a', b', c' are elements of a pencil with center P'. Use dynamic geometry software to construct the projectivity such that abc is projectively related to a'b'c'.
The construction of the projectivity in the following illustration consists of the
perspectivities
and
where the pencil of lines containing a', b1, c has center a'
· c. Click
here for a dynamic illustration.
