options: Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
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
$${\overleftrightarrow {CA} \parallel \overleftrightarrow {DB}}$$
.


correct_option_index: 1