16-2: Proving a Quadrilateral is a Rectangle Objectives: Assignment: To prove that a

16-2: Proving a Quadrilateral is a Rectangle
Objectives:
1. To prove that a
quadrilateral is a
rectangle
Assignment:
• P. 229: 12-17
• P. 235: 7-11
Objective 1
You will be able to prove
that a quadrilateral is
a rectangle
Rectangles
A rectangle is
an equiangular
parallelogram.
Example 1
What must each angle of a rectangle
measure?
Rectangle Corollary
A quadrilateral is a
rectangle if and only
if it has four right
angles.
Example 2
The Rectangle Corollary is a biconditional
statement. Write the two if-then statements
that compose this theorem.
A quadrilateral is a rectangle if and only if it
has four right angles.
Example 3
Prove the Rectangle Corollary. Note that
this proof should justify both statements in
the biconditional statement.
A quadrilateral is a rectangle if and only if it
has four right angles.
If a quadrilateral is a rectangle,
then it has four right angles.
If a quadrilateral has four right angles,
then it is a rectangle.
Example 4
Prove the following theorem:
If a parallelogram has one right angle, then it
is a rectangle.
Rectangle Diagonal Theorem
A parallelogram is a rectangle if and only if
its diagonals are congruent.
Example 5
You’ve just had a new door installed, but it
doesn’t seem to fit into the door jamb
properly. What could you do to determine
if your new door is rectangular?
Example 6
The Rectangle Diagonal Theorem is a
biconditional statement. Write the two if-then
statements that compose this theorem.
A parallelogram is a rectangle if and only if its
diagonals are congruent.
Example 7
Prove the Rectangle Diagonal Theorem.
Note that this proof should justify both
statements in the biconditional statement.
A parallelogram is a rectangle if and only if its
diagonals are congruent.
If a parallelogram is a rectangle,
then its diagonals are congruent.
If a parallelogram’s diagonals are
congruent, then it is a rectangle.
Example 8
Classify the quadrilateral 𝐴𝐵𝐶𝐷.
1. A(1, 0), B(0, 3), C(6, 5), and D(7, 2)
2. A(1, 1), B(1, 6), C(10, 9), and D(13, 5)
16-2: Proving a Quadrilateral is a Rectangle
Objectives:
1. To prove that a
quadrilateral is a
rectangle
Assignment:
• P. 229: 12-17
• P. 235: 7-11