of a rectangle are congruent."
A Proof Outline
by David Wise
Note: I recommend that this page be printed out, so that the
instructions are easier to follow.
In order to successfully complete a proof,
it is important to think of the definition and the construction
of a rectangle.
In the following outline, I will provide the statements, you
provide the reasons.
Prove: If a quadrilateral is a rectangle, then
the diagonals of the rectangle are congruent.
Given: Rectangle ABCD with diagonals AC and
Prove: Segment AC is congruent
to segment BD.
- A rectangle is a parallelogram, so the definition
and properties of a parallelogram apply to a rectangle.
- Consider how a rectangle is constructed------parallel
- Consider properties of parallel lines.
- Consider triangle congruency properties.
- Click here to investigate this sketch to help with the steps
of the proof.
First we will look at only one diagonal.
- Angle DCA is congruent to angle BAC.
- Angle ADC is congruent to angle CBA.
- Triangle ADC is congruent to triangle CBA.
- Segment AD is congruent to segment BC.
Then we will look at both diagonals.
- Angle BAD is congruent to angle CBA.
- Segment AB is congruent to segment AB.
- Triangle DAB is congruent to triangle CBA.
- Segment AC is congruent to segment
- Transform the two-column
proof into a paragraph proof.
- Find an alternative way to
prove that the diagonals of a rectangle are congruent.
If you have any questions while trying to complete this investigation,
or suggestions that would be useful, especially for use at the
high school level, please send e-mail to firstname.lastname@example.org.
the Table of Contents.