standard_description: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
problem_activity: Suppose
$${{\overline{AB}}}$$
is a line segment and
D
is a point not on
$${{\overline{AB}}}$$
as pictured below.
[IMG]
Let
C
be the point so that
$${CD=AB}$$
,
$${\overleftrightarrow {CD} \parallel \overleftrightarrow {AB}}$$
and
ABCD
is a quadrilateral.
Draw
$${\overline {CD}}$$
using constructions.
Explain how you know that
$${\overleftrightarrow {CA} \parallel \overleftrightarrow {DB}}$$
.


aligns: yes