WHAT DO YOU CALL A

1
WHAT DO YOU CALL A CRUSHED ANGLE ?
A
RECTANGLE
2
Theorem 6-9 If a parallelogram is a rectangle,
then its diagonals are congruent.
Given ABCD is a rectangle. Prove AC ? BD
A
B
C
D

• Proof
• Parallelogram ABCD is a rectangle. 1) Given
• AB ? CD, AD ? CB 2) In a parallelogram
• 
  opposite sides are ?.
• ?ABC is a right angle. 3) Definition of
  rectangle
• ?CDA is a right angle.
• ?ABC ? ?CDA 4) SAS Postulate
• AC ? BD

3
A LITTLE ACORN FELL FROM A TREE. IT SPROUTED
ROOTS THAT DUG DEEP INTO THE DEEP, RICH SOIL.
FOR YEARS IT GREW AND GREW AND GREW. WHAT DID IT
PROUDLY SAY?
E
E
G
T
Y
R
O
M
4
Use a straightedge to draw line l. Label point J
on line l.
J
l
5
With your compass set at 6 cm, place the point of
the compass at J and locate point K on l so that
JK 6cm.
J
K
l
6 cm
6
Now construct lines perpendicular to l through J
and through K. Label them m and n.
m
n
J
K
l
6 cm
7
Set your compass at 3 cm. Place the compass
point at K and mark off a segment on n. Using
the same compass setting, place the compass at J
and mark a segment on m. Label these points O
and P.
m
n
O
P
3 cm
3 cm
J
K
l
6 cm
8
Draw OP.
n
m
O
P
3 cm
3 cm
J
K
l
6 cm
9
Quadrilateral JKPO is a parallelogram, and all
angles are right angles. Therefore,
quadrilateral JKPO is a rectangle with a length
of 6 cm and a width of 3 cm.
m
n
O
P
3 cm
3 cm
J
K
l
6 cm
10
Locate the compass setting that represents JP and
compare to the setting for OK. The measures
should be the same.
m
n
O
P
3 cm
3 cm
J
K
l
6 cm
11
Theorem 6 9 If a parallelogram is a
rectangle, then its diagonals are congruent.
12
WHAT DO YOU CALL A MAN THAT GOES TO THE BEACH A
LOT?
A
TAN
GENT
!
13
Theorem 6 10
If the diagonals of a parallelogram are
congruent, then the Parallelogram is a rectangle.
B
A
Given ABCD is a parallelogram AC ? BD Prove
ABCD is a rectangle
Oh yeah!
There's more!!!
D
C

• Proof
• AC ? BD 1. Given
• AB CD, BC DA, 2. Definition of
• Parallelogram
• ?ABC, ?CDA, ?BAD, ?DCB 3. SSS
• ? BAD, ?ABC, ?BAD, ?DCB 4. CPCTC
• ?BAD, ?ABC, ?BAD, ?DCB 5. Def of congruent
  angles

14
But, not a lot more!!!
15
B
A
C
D

• 4(? BAD)360 6. The sum of the angles in
• a rectangle is 360.
• 7. ? BAD 90 7. Division of equality
• 8. ? ABC, ? CDA, ? DCB 90 8. Substitution of
  equality
• 9. ABCD is a rectangle 9. Definition of
  Rectangle

FINISHED
16
QUICK QUIZ
M
N

• MO 2X 8 NP 23
• Find the value of X.
• MQ 3X 7 NP 26
• Find the value of X.
• T or F ?
• If a quadrilateral has opposite sides that
  are congruent,
• then it is a rectangle. Justify your
  answer.

X 15.5
Q
X 2
P
O
If a quadrilateral has opposite sides that are
congruent then it is a PARALLELOGRAM, not
necessarily a rectangle. F A L S E